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The aim of this paper is to develop an unconditionally stable Euler implicit/explicit scheme for the natural convection equations based on an introduced exponential scalar auxiliary variable. Our numerical scheme involves treating the linear terms in the implicit scheme and nonlinear terms in the explicit scheme. Then, the considered problem is decoupled into a series of linearized subproblems, and these algebraic systems with constant coefficient matrixes can be solved efficiently. Compared with the existing theoretical findings of the implicit/explicit scheme for the incompressible flow [He YN. The Euler implicit/explicit scheme for the 2D time-dependent Navier-Stokes equations with smooth or nonsmooth initial data. Math Comput. 2008;77(264):2097–2124.; He YN, Huang PZ, Feng XL. H2-stability of first order fully discrete schemes for the time-dependent Navier-Stokes equations. J Sci Comput. 2015;62:230–264; He YN, Li J. A penalty finite element method based on the Euler implicit/explicit scheme for the time-dependent Navier-Stokes equations. J Comput Appl Math. 2010;235(3):708–725; Jin JJ, Zhang T, Li J. H2 stability of the first order Galerkin method for the Boussinesq equations with smooth and nonsmooth initial data. Comput Math Appl. 2018;75(1):248–288; Su J, He YN. The almost unconditional convergence of the Euler implicit/explicit scheme for the three dimensional nonstationary Navier-Stokes equations. Discrete Continuous Dyn Syst Ser B. 2017;22(9):3421–3438], our analysis removes the restriction on time step Δ t ≤ C , and obtains the unconditional stability and convergence theoretical findings. Some numerical results are also provided to verify the established theoretical analysis and show the performances of the considered numerical scheme. [ABSTRACT FROM AUTHOR]

This paper considers the two-level iterative finite element methods for the steady natural convection equations under some uniqueness conditions with the Simple-, Oseen- and Newton-type corrections. Firstly, the stability and convergence of the one-level iterative finite element methods are analyzed under some restrictions on physical parameters. Secondly, under the strong uniqueness condition, we develop the two-level finite element method with Simple, Oseen and Newton iterations of m times on the coarse mesh τ H with mesh size H, and then, the considered problem is linearized in three correction schemes with the Simple, Oseen and Newton corrections one time on the fine grid τ h with mesh size h ≪ H based on the obtained iterative solutions. From the theoretical point of view, the results obtained by the two-level iterative methods have the same precision as those obtained by the one-level method which mesh sizes satisfy h = O (H 2) and the iterative steps are greater than some constants. Thirdly, the stability and convergence of one-level Oseen iterative scheme with respect to the mesh size and the iterative time m are provided under a weak uniqueness condition. Finally, some numerical experiments are designed to confirm the established theoretical findings and verify the performance of the proposed numerical schemes. [ABSTRACT FROM AUTHOR]

This paper considers the stability and convergence of Euler implicit/explicit scheme for the incompressible magnetohydrodynamic (MHD) equations by the scalar auxiliary variable approach. The linear and nonlinear terms are treated by the implicit and explicit schemes, respectively, then the considered problem is split into two constant coefficient linear algebraic equations plus a nonlinear algebraic equation. Compared with the original discrete coefficient matrix, the computational size reduce and we can solve these subproblems conveniently and efficiently. First, an equivalent form of the MHD problem with four variables is developed, the corresponding stability and convergence results of spatial discrete scheme are presented. Second, the decoupled and linearized auxiliary variable finite element method is constructed, the discrete unconditional energy dissipation and stability of uhn and Hhn in various norms are established. The optimal error estimates of numerical solutions in L2 and H‐norms are also developed by the energy method and Gronwall lemma. Finally, some numerical examples are presented to verify the established theoretical findings and show the performances of the considered numerical algorithm. [ABSTRACT FROM AUTHOR]

Programming the shape of soft smart materials is a challenging task due to the enormous design space involved. In this study, we propose a novel approach to determine applied stimuli that enable the desired actuated shapes of soft smart materials. Our approach combines finite element methods (FEM), deep neural networks (DNN), and particle swarm optimization (PSO). By employing beams made of dielectric elastomer (DE) as models, we partition a DE beam into multiple actuating units, allowing independent actuation through the application of paired electrical stimuli. FEM is subsequently employed to compute the actuated shapes in response to various applied stimuli. The selection of these stimuli is accomplished through the utilization of Latin hypercube sampling. By utilizing the FEM-derived data, we have developed a machine learning (ML) surrogate model that integrates a long short-term memory (LSTM) network with a fully connected neural network (FCNN). Finally, PSO is employed to determine the optimal applied stimulus that yields the desired actuated shape. The LSTM-FCNN surrogate model is utilized to evaluate the fitness of PSO. The ML-PSO framework exhibits remarkable performance and efficiency in the context of the inverse design of soft smart beams. [Display omitted] • Nonlinear FEM is employed to accurately capture the relationship between the actuated shape and external stimuli of dielectric elastomers. • Machine learning surrogate models enable fast and highly accurate prediction of shape morphing. • The combination of particle swarm optimization and machine learning proves to be efficient in designing the shape of soft smart beams. • This approach can be applied to control soft beam robots under various types of stimuli. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Galerkin finite element method (FEM) for the Kelvin-Voigt viscoelastic fluid flow model with the lowest equal-order pairs. In order to overcome the restriction of the so-called inf-sup conditions, a pressure projection method based on the differences of two local Gauss integrations is introduced. Under some suitable assumptions on the initial data and forcing function, we firstly present some stability and convergence results of numerical solutions in spatial discrete scheme. By constructing the dual linearized Kelvin-Voigt model, stability and optimal error estimates of numerical solutions in various norms are established. Secondly, a fully discrete stabilized FEM is introduced, the backward Euler scheme is adopted to treat the time derivative terms, the implicit scheme is used to deal with the linear terms and semi-implicit scheme is applied to treat the nonlinear term, unconditional stability and convergence results are also presented. Finally, some numerical examples are presented to verify the developed theoretical analysis and show the performances of the considered numerical schemes. [ABSTRACT FROM AUTHOR]

The objective of this paper is to establish the unconditional stability results of Euler implicit/explicit scheme for the viscoelastic Kelvin–Voigt model with a scalar auxiliary variable. We first reformulate the Kelvin–Voigt model into an equivalent system with three variables. The standard Galerkin finite element method is used to approximate the spatial discretization. Then the Euler implicit/explicit method is adopted to discrete the considered problem, a constant coefficient algebraic system is formed and it can be solved efficiently. The unconditional energy dissipation and stability results of numerical solutions in various norms are established. Optimal error estimates are also presented by the energy method and the Gronwall lemma. Finally, some numerical results are given to verify the established theoretical findings and show the performances of the considered numerical scheme. [ABSTRACT FROM AUTHOR]

Live working in distribution work is an important way to ensure normal power supply of power equipment. Live installation tool for robot operation was proposed in this paper in order to reduce the safety accidents occurrence. Through different structures and sensor combinations, it can complete the autonomous operation by cooperating with robot, including lead wire monitoring, line detection and tightening the puncture clamp. Finally, the finite element analysis of gear transmission was carried out, and the results showed that the design of the tool can mees the strength requirements. [ABSTRACT FROM AUTHOR]

In this paper, we consider the space‐time finite element method for the viscoelastic Kelvin‐Voigt model. Firstly, based on a priori estimates of spatial semidiscrete numerical solutions, stability and convergence results of one‐level space‐time finite element solutions in different norms are provided under some restrictions on the time step. Secondly, in order to improve the computational efficiency, multilevel space‐time finite element method is introduced. In the multilevel numerical scheme, the nonlinear Kelvin‐Voigt problem is just solved in the coarsest mesh, the Newton iteration is adopted to treat the nonlinear term, and a series of linear Kelvin‐Voigt problems are considered in successive shape conforming regular triangulations. The multilevel space‐time finite element approximate solution is shown to have a convergence rate of the same order as that of the one‐level space‐time finite element solutions of the nonlinear Kelvin‐Voigt problem on a fine mesh with some appropriate choices between the time steps and mesh sizes: kj∼kj−12,hj∼hj−13/2. Finally, some numerical results are provided to verify the established theoretical findings. Compared with the standard Galerkin finite element method, from the view point of theoretical analysis, the space‐time finite element method has the same convergence orders for variables as the Galerkin method. However, from the view point of numerical simulations, the space‐time finite element method improves the computational accuracy without additional computational cost. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Crank‐Nicolson extrapolation scheme for the 2D/3D unsteady natural convection problem. Our numerical scheme includes the implicit Crank‐Nicolson scheme for linear terms and the recursive linear method for nonlinear terms. Standard Galerkin finite element method is used to approximate the spatial discretization. Stability and optimal error estimates are provided for the numerical solutions. Furthermore, a fully discrete two‐grid Crank‐Nicolson extrapolation scheme is developed, the corresponding stability and convergence results are derived for the approximate solutions. Comparison from aspects of the theoretical results and computational efficiency, the two‐grid Crank‐Nicolson extrapolation scheme has the same order as the one grid method for velocity and temperature in H1‐norm and for pressure in L2‐norm. However, the two‐grid scheme involves much less work than one grid method. Finally, some numerical examples are provided to verify the established theoretical results and illustrate the performances of the developed numerical schemes. [ABSTRACT FROM AUTHOR]

Presents information on a study that examined critical epilayer thickness for the formation of misfit dislocations at the interface between an epilayer and a substrate with finite thickness. Theoretical analysis on stress distribution; Details on the contours of stress components arising from an edge dislocation; Conclusion.

Abstract In this paper, we consider the parallel two-grid finite element method for the transient natural convection problem with non-smooth initial data. Our numerical scheme involves solving a nonlinear natural convection problem on the coarse grid and solving a linear natural convection problem on the fine grid. The linear natural convection problem can be split into two subproblems which can be solved in parallel: a linearized Navier–Stokes problem and a linear parabolic problem. We firstly provide the stability and convergence of standard Galerkin finite element method with non-smooth initial data. Secondly, we develop optimal error estimates of two-grid finite element method for velocity and temperature in H 1 -norm and for pressure in L 2 -norm. In order to overcome the difficulty posed by the loss of regularity, some suitable weight functions are introduced in our stability and convergence analysis for the natural convection equations. Finally, some numerical results are presented to verify the established theoretical results. [ABSTRACT FROM AUTHOR]

Based on the mixed finite element method, we consider the decoupled Crank-Nicolson/Adams-Bashforth scheme for the Boussinesq equations with smooth initial data in this paper. The temporal treatment of the spatial discrete Boussinesq equations is based on the implicit Crank-Nicolson scheme for the linear terms and the explicit Adams-Bashforth scheme for the nonlinear terms. Thanks to the decoupled method, the considered problem is split into two subproblems and these subproblems can be solved in parallel. Under some restriction on the time step, we present the stability and convergence results of numerical solutions, Finally, some numerical experiments are provided to test the performance of the developed numerical scheme and verify the established theoretical findings. [ABSTRACT FROM AUTHOR]

Remote geovisualization has gained momentum to support large‐scale geospatial data analysis and complex decision‐making over the last few years. Cloud computing, due to its capabilities to deliver on‐demand computing resources, has been embraced to develop and deploy interactive and scalable remote geovisualization applications. However, current cloud computing frameworks do not offer a versatile resource management scheme that is readily applicable for online remote visualization services, which usually require maintaining a satisfactory service level over time under dynamic workloads. To address this gap, we propose an automatic cloud resource management approach based on a bi‐level scheduling and horizontal scaling scheme to exploit cloud resources efficiently. At the lower level, a dynamic task‐scheduling scheme using collaborative filtering techniques is proposed to allocate virtual cloud resources to execute sub‐tasks. The scheduling scheme considers spatio‐temporal patterns presented in visualization views. At the upper level, reinforcement learning is adopted to perform resource auto‐scaling based on a reward function that integrates three different facets, namely: time cost, resource cost, and service stability. The original reinforcement learning algorithm is improved in two main aspects: (1) considering the delay of resource provisioning that is common in cloud environments; and (2) using online Gaussian estimation to estimate Q values. Task scheduling and auto‐scaling interact with each other and are integrated to deliver a comprehensive and responsive resource management solution. Experimental results demonstrate that our approach outperforms several existing cloud resource management methods. The proposed approach is also applicable for other interactive visualization applications, which have similar workload characteristics and performance requirements as interactive remote geovisualization. [ABSTRACT FROM AUTHOR]

In this paper, the decoupled Crank–Nicolson/Adams–Bashforth scheme for the Boussinesq equations is considered with nonsmooth initial data. Our numerical scheme is based on the implicit Crank–Nicolson scheme for the linear terms and the explicit Adams–Bashforth scheme for the nonlinear terms for the temporal discretization, standard Galerkin finite element method is used to the spatial discretization. In order to improve the computational efficiency, the decoupled method is introduced, as a consequence the original problem is split into two linear subproblems, and these subproblems can be solved in parallel. We verify that our numerical scheme is almost unconditionally stable for the nonsmooth initial data ( u 0 , θ 0 ) with the divergence-free condition. Furthermore, under some stability conditions, we show that the error estimates for velocity and temperature in L 2 norm is of the order O ( h 2 + Δ t 3 2 ) , in H 1 norm is of the order O ( h 2 + Δ t ) , and the error estimate for pressure in a certain norm is of the order O ( h 2 + Δ t ) . Finally, some numerical examples are provided to verify the established theoretical findings and test the performances of the developed numerical scheme. [ABSTRACT FROM AUTHOR]

In this article, we develop several first order fully discrete Galerkin finite element schemes for the Oldroyd model and establish the corresponding stability results for these numerical schemes with smooth and nonsmooth initial data. The stable mixed finite element method is used to the spatial discretization, and the temporal treatments of the spatial discrete Oldroyd model include the first order implicit, semi‐implicit, implicit/explicit, and explicit schemes. The H 2 ‐stability results of the different numerical schemes are provided, where the first‐order implicit and semi‐implicit schemes are the H 2 ‐unconditional stable, the implicit/explicit scheme is the H 2 ‐almost unconditional stable, and the first order explicit scheme is the H 2 ‐conditional stable. Finally, some numerical investigations of the H 2 ‐stability results of the considered numerical schemes for the Oldroyd model are provided to verify the established theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we consider the stability and convergence results of numerical solutions in fully discrete fractional-step formulation for the Oldroyd model. The proposed numerical method is constructed by the decompositions of the viscosity in time part and the finite element method in space part. With some mild regularity assumptions on the exact solution, the unconditional stability results of the approximate solutions are established. Then, the first order spatial convergence for the “end-of-step” velocity is shown. Based on the above results, the optimal order approximations for the velocity and pressure in L 2 -norm are obtained for the mesh size. Finally, two numerical examples are given to illustrate the established theoretical analysis and test the performances of the developed numerical method and show the influences of the memory term for the considered problem. [ABSTRACT FROM AUTHOR]

Previous works on the convergence of numerical methods for the Boussinesq problem were conducted, while the optimal L2‐norm error estimates for the velocity and temperature are still lacked. In this paper, the backward Euler scheme is used to discrete the time terms, standard Galerkin finite element method is adopted to approximate the variables. The MINI element is used to approximate the velocity and pressure, the temperature field is simulated by the linear polynomial. Under some restriction on the time step, we firstly present the optimal L2 error estimates of approximate solutions. Secondly, two‐level method based on Stokes iteration for the Boussinesq problem is developed and the corresponding convergence results are presented. By this method, the original problem is decoupled into two small linear subproblems. Compared with the standard Galerkin method, the two‐level method not only keeps good accuracy but also saves a lot of computational cost. Finally, some numerical examples are provided to support the established theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, the H 2 -stability of the first order fully discrete Galerkin finite element methods for the Boussinesq equations with smooth and non-smooth initial data is presented. The finite element spatial discretization for the Boussinesq equations is based on the mixed finite element method, and the temporal treatments of the spatial discrete Boussinesq equations include the implicit scheme, the semi-implicit scheme, the implicit/explicit scheme and the explicit scheme. The H 2 -stability results of the above numerical schemes are established. Firstly, we prove that the implicit and semi-implicit schemes are the H 2 -unconditional stable. Then we show that the implicit/explicit scheme is H 2 -almost unconditional stable with the initial data that belong to H 1 and H 2 , and the similar results are obtained for the semi-implicit/explicit scheme in the case of the initial data that belong to L 2 . Furthermore, we show that the explicit scheme is the H 2 -conditional stable. Finally, some numerical examples are provided to verify the established theoretical findings and confirm the corresponding H 2 stability analysis of the different numerical schemes. [ABSTRACT FROM AUTHOR]

In this paper, we consider the posteriori error estimates of Galerkin finite element method for the unsteady Navier–Stokes equations. By constructing the approximate Navier–Stokes reconstructions, the errors of velocity and pressure are split into two parts. For the estimates of time part, the energy method and other skills are used, for the estimates of spatial part, the well-developed theoretical analysis of posteriori error estimates for the elliptic problem can be adopted. More important, the error estimates of time part can be controlled by the estimates of spatial part. As a consequence, the posteriori error estimates in L ∞ (0, T ; L 2 (Ω)),  L ∞ (0, T ; H 1 (Ω)) and L 2 (0, T ; L 2 (Ω)) norms for velocity and pressure are derived in both spatial discrete and time-space fully discrete schemes. [ABSTRACT FROM AUTHOR]

In the paper we consider the one-level and two-level iterative penalty finite element methods for the steady incompressible magnetohydrodynamic problem based on the iteration of pressure with a factor of penalty parameter. Firstly, the $$\mathbf {H}^1$$ and $$\mathbf {L}^2$$ error estimates of numerical solutions of one-level iterative penalty finite element method are provided. Secondly, the stability and convergence of two-level iterative penalty finite element method are analyzed. Finally, some numerical results are provided to verify the effectiveness of the developed numerical schemes. [ABSTRACT FROM AUTHOR]

In this paper, the decoupled stabilized finite element methods are developed for the Boussinesq equations with temperature dependent coefficients. In our numerical schemes, the original problem is decoupled into the linearized Navier-Stokes equations and a parabolic problem, the low order mixed finite element pairs are used to approximate the spatial spaces and the backward Euler scheme is adopted to treat the time terms. Furthermore, the linear terms are dealt with the implicit scheme while the nonlinear terms are treated by the semi-implicit scheme, then, a lot of storage and computational cost are saved. The advantages for our numerical schemes are parameter-free, unconditionally stable, and constant matrix at each time level. Finally, some numerical tests are presented to verify the theoretical results of the developed numerical methods, and show that our schemes not only keep good accuracy but also save a lot of computational times. [ABSTRACT FROM AUTHOR]

In this paper, a finite element variational multiscale method (VMM) is developed for the stationary incompressible magnetohydrodynamics (MHD) problem and the corresponding stability and convergence are established. Our VMM is based on the polynomial bubble functions as a subgrid scale and the numerical implementation is based on the local Gauss integrations. Compared to the common VMM, our method does not introduce any extra variable. Furthermore, the two-level finite element VMM is also developed. Compared to the one-level VMM, the two-level VMM consists of solving a nonlinear MHD problem on a coarse mesh with mesh sizeH, and then a linearized magnetohydrodynamic problem based on the Oseen iteration on a fine mesh is solved with mesh size. Stability and convergence of numerical approximations in two-level VMM are presented. Finally, some numerical examples are provided to demonstrate the effectiveness of the developed numerical algorithms. [ABSTRACT FROM AUTHOR]

• This paper considers the first order semi-implicit energy stable finite element method for the two phase magnetohydrodynamic flows (the Cahn–Hilliard equation coupling the incompressible MHD system), some numerical results are provided to show the performances of the considered numerical scheme. The main contribution of this work is to present the rigorous unconditional stability of numerical solutions in both time semi-discrete and fully discrete cases with two suitable stabilized terms. Optimal error estimates of numerical solutions are also presented by using the energy method and the Gronwall lemma. Our findings enrich and develop the theoretical analysis results of mixed finite element for the two-phase incompressible flows. This paper is devoted to present the rigorous unconditional stability and optimal error estimates of first order semi-implicit energy stable finite element method developed by Yang et al. (Comput. Methods Appl. Mech. Engrg. 356 (2019) 435–464) for the two phase magnetohydrodynamic(MHD) flows, some numerical results are also provided to show the performances of the considered numerical scheme. [ABSTRACT FROM AUTHOR]

For the time-dependent thermal convection problems with temperature-dependent coefficients, the implicit–explicit scheme is presented, in which mixed finite element method is applied for the spatial approximation of the velocity, pressure and temperature while the time discretization is based on the high-order backward difference scheme. Linear terms are dealt with the implicit scheme while the nonlinear terms are treated by the semi-implicit scheme. The advantages for this scheme are unconditionally stable, decoupled computational and second order accuracy. Finally, numerical tests illustrate the theoretical results of the presented schemes, and display that the highly efficient method conserves the property of divergence free of the original problems. [ABSTRACT FROM AUTHOR]

In this paper, we consider the posteriori error estimates of fully discrete finite element method for the time-dependent Oseen equations. By constructing an appropriate Oseen reconstruction, the optimal error estimates inandnorms for velocity and pressure are derived in spatial semidiscrete scheme. Furthermore, a fully discrete scheme is studied based on the backward Euler scheme and the corresponding posteriori error estimators are derived. Finally, some numerical results are presented to verify the performance of the established posteriori error estimators. [ABSTRACT FROM AUTHOR]

In the paper we consider the penalty finite element method for the stationary incompressible magnetohydrodynamics (MHD) problem with a factor of penalty parameter. Stability and convergence of numerical solutions are established. Furthermore, two level penalty methods are also developed for the MHD problem. Our methods consist of solving a nonlinear MHD problem by the usual penalty method on a coarse mesh with mesh size H , and then a linearized MHD problem based on the Stokes, Newton and Oseen iterations on a fine mesh is solved by the penalty method with mesh size h ( h ≪ H ) , respectively. Stability and error estimates of numerical solutions in two level penalty methods are presented. Finally, some numerical tests are provided to demonstrate the effectiveness of the developed algorithms. [ABSTRACT FROM AUTHOR]

In this article, a decoupled two grid finite element method (FEM) is proposed and analyzed for the nonsteady natural convection problem using the coarse grid numerical solutions to decouple the nonlinear coupled terms, and the corresponding optimal error estimates are derived. Compared with the standard Galerkin FEM and the usual two-grid FEM, our algorithm not only keeps good accuracy but also saves a lot of computational cost. Some numerical examples are provided to verify the performances of the decoupled two-grid FEM. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the decoupled two-grid FEM for the nonsteady natural convection problem. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 2135-2168, 2015 [ABSTRACT FROM AUTHOR]

In this work three kinds of decoupled two level finite element methods are proposed and analyzed for the natural convection problem. Firstly, some a priori bounds and the optimal error estimates of velocity and temperature in L norm are provided for the standard Galerkin finite element method. Secondly, by using the coarse grid numerical solutions to decouple the nonlinear coupling term, we establish the convergence results for the proposed decoupled two level finite element schemes with meshes h and H satisfy h= H. Finally, two numerical examples are presented to show the efficiency and effectiveness of the proposed algorithms for the steady natural convection problem. [ABSTRACT FROM AUTHOR]

Evaluation of the NVH (noise, vibration and harshness) performance of automotive powertrain has been an integral part of the vehicle development process. Although electric vehicles are generally considerably quieter than their counterparts powered by internal combustion engines, some problems about NVH still exist, which are becoming more challenging in terms of the future of vehicle. Firstly, the sound only from dominant engine but not from tire, wind or auxiliaries disappears, which consequently becomes increasingly audible due to the removal of the masking sound of broadband engine. Moreover, the interior noise is characterized by high-frequency noise components which can be subjectively perceived as annoying and unpleasant. Thirdly, as the electric vehicle develops toward the direction of high speed and large torque, electric vehicle vibration and noise problems highlight gradually. The subject of this paper is the numerical and experimental evaluation of the acoustic behavior of an electric powertrain, which is helpful for the electric vehicle in the design stage. For this purpose, a co-simulation method based on finite element modeling (FEM) and boundary element method (BEM) for the acoustic radiation analysis of an electric powertrain under multi-excitations is presented. The vibration and noise characteristics of electric vehicle are quite different from that of internal combustion engine due to different exciting forces. The calculation of the internal excitations of motor-reducer integrated drive system is the foundation of dynamic analysis. The internal dynamic excitations of a certain electric powertrain in rated revolution are calculated by theoretical analysis and numerical simulation method on the basis of gear dynamics and electromagnetism, including the electromagnetic radial force, electromagnetic tangential force and external circuit in the motor, and the time-varying gear meshing stiffness, meshing error and meshing impact in the gear system. The amplitude of the electromagnetic forces is concentrated on the current harmonic frequencies, while the gear meshing force is on the meshing frequencies. On this basis, a structural dynamic model is established based on FEM to carry out the vibration modal analysis and calculate the vibration responses. The analysis shows that the electric motor can be influenced by the reducer, which makes the NVH characteristics of the electric motor are totally different from that without reducer. Then, an acoustic model of the electric powertrain is established based on BEM to calculate the radiated sound pressure with the results of vibration response analysis, in order to find out its effect on the acoustic radiation. From the contour graph of different field points' acoustic pressures, it can be learnt that sound pressure level of radiation noise near motor and reducer is higher than any other places and radiation noise spreads in radial lines. In order to testify the theoretical analysis, an experimental bench is used to test the radiation noise of the electric powertrain in a semi-anechoic chamber. The results derived from both simulation and experiment indicate that the 6th and 12th harmonics of current are the main reasons of making electromagnetic noise, and meanwhile the gear's active meshing frequency as well as its doubling and tripling frequencies contributes to the gear whining. Thus, a template from end to end to predict NVH performance of an electric powertrain has been established. The results can provide a beneficial support for the further study of electric powertrain noise control. [ABSTRACT FROM AUTHOR]

A bilayer beam model is extended to study the fracture behavior of dielectric interfacial cracks. In this model, a semi-infinite crack with an original opening value is oriented along the interface between two dielectric layers which are under mechanical/electrical loading. Taking into account the effect of the electrostatic traction on the interfacial crack, a nonlinear analytical solution is derived, along with also a developed finite element analysis method where a special constitutive equation for the capacitor element in ANSYS is utilized to simulate the electrostatic tractions. Both the analytical and numerical solutions predict the same results which further show that the elastic and dielectric mismatches can play a significant role in the interfacial cracking behavior under mechanical and electrical loading. Furthermore, the electrostatic tractions may cause hysteresis loops in the curve of crack opening versus applied mechanical displacement or versus applied electric voltage. An applied mechanical load is the driving force for the interfacial cracking, while an applied electric field retards it. [ABSTRACT FROM AUTHOR]

In this work, we systematically analyze a stabilized finite volume method for the Poisson equation. On stating the convergence of this method, optimal error estimates in different norms are obtained by establishing the adequate connections between the finite element and finite volume methods. Furthermore, some super-convergence results are established by using L2-projection method on a coarse mesh based on some regularity assumptions for Poisson equation. Finally, some numerical experiments are presented to confirm the theoretical findings. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we develop a posteriori error estimates for the steady Navier–Stokes equations based on the lowest equal-order mixed finite element pair. Residual type a posteriori error estimates are derived by means of general framework established by Verfürth for the nonlinear equations. Furthermore, a simple error estimator in norm is also presented by using the duality argument. Numerical experiments using adaptive computations are presented to demonstrate the effectiveness of these error estimates for three examples. The first example is a singular problem with known solution, the second example is a physical model of lid driven cavity and the last one is a backward facing step problem. [Copyright &y& Elsevier]

In this work, we consider a stabilised characteristic finite element method for the time-dependent Navier-Stokes equations based on the lowest equal-order finite element pairs. The diffusion term in these equations is discretised by using finite element method, the temporal differentiation and advection terms are treated by characteristic schemes. Unconditionally stable results and error estimates of optimal order for the velocity and pressure are established. Finally, some numerical results are provided to verify the performance of this method. [ABSTRACT FROM AUTHOR]

In this paper, the stability and convergence results of finite volume method for the time-dependent incompressible magnetohydrodynamics equations are developed based on triangulation. The linear polynomials are used to approximate the velocity, magnetic fields and pressure. In order to overcome the restriction of the discrete inf-sup condition, the local pressure projection method is employed. Firstly, two self-adjoint linear mappings are introduced to establish the equivalences of temporal terms and bilinear terms in finite element method and finite volume method. Secondly, the existence and uniqueness of numerical solutions are presented by using the Oseen iteration and mathematical induction method. Thirdly, H 2 -stability and optimal error estimates are provided by introducing the Galerkin projection of generalized bilinear terms in finite volume method, using the energy method and constructing the corresponding dual problem. The main theoretical findings of this paper are as follows: ‖ (u h (t) , H h (t)) ‖ 0 2 + ∫ 0 t (min ⁡ { ν , γ σ − 1 } ‖ (u h , H h) ‖ 1 2 + G (p h , p h)) d s ≤ C , min ⁡ { ν , γ σ − 1 } ‖ (u h (t) , H h (t)) ‖ 1 2 + G (p h (t) , p h (t)) + ∫ 0 t ‖ (u h t , H h t) ‖ 0 2 d s ≤ C , ‖ ∇ (u h , H h) ‖ 0 2 + ∫ 0 t min ⁡ { ν , γ σ − 1 } ‖ (A 1 h u h , A 2 h H h) ‖ 0 2 d s ≤ C , τ 1 2 (t) ‖ (u (t) − u h (t) , H (t) − H h (t)) ‖ 0 + h (‖ (u (t) − u h (t) , H (t) − H h (t)) ‖ 1 + τ 1 2 (t) ‖ p (t) − p h (t) ‖ 0) ≤ C h 2 , where τ (t) = min ⁡ { 1 , t } , the letters ν , σ are the physical parameters, C and γ are two positive constants independent of the mesh size h , (u , H , p) and (u h , H h , p h) are the solutions of problems (2.1) and (4.1). Finally, some numerical results are presented to verify the established theoretical findings and show the performances of the considered numerical method. [ABSTRACT FROM AUTHOR]

In this paper, based on the pressure project method, we consider an adaptive stabilized finite volume method for the Oseen equations with the lowest equal order finite element pair. Firstly, we develop the discrete forms in both finite element and finite volume methods, and establish the existence and uniqueness of numerical solutions by establishing the equivalence of linear terms in finite element and finite volume methods. Secondly, a residual type a posteriori error estimator is designed, and the computable global upper and local lower bounds between the exact solutions and the finite volume solutions are established. Thirdly, a discrete local lower bound between two successive finite volume solutions is obtained, convergence analysis of the adaptive stabilized finite volume method is also performed. Finally, some numerical results are presented to verify the performances of the developed error estimators and confirm the established theoretical findings. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a fully discrete defect-correction mixed finite element method (MFEM) for solving the non-stationary conduction–convection problems in two dimension, which is leaded by combining the Back Euler time discretization with the two-step defect correction in space, is presented. In this method, we solve the nonlinear equations with an added artificial viscosity term on a finite element grid and correct these solutions on the same grid using a linearized defect-correction technique. The stability and the error analysis are derived. The theory analysis shows that our method is stable and has a good convergence property. Some numerical results are also given, which show that this method is highly efficient for the unsteady conduction–convection problems. [Copyright &y& Elsevier]

Abstract: In this article, new one- and two-level Newton iterative mixed finite element methods (MFEM) for two-dimensional stationary conduction–convection problems are presented. In both of the methods, we decouple the conduction–convection problem into two systems: one is for the temperature and the other is for the velocity and pressure. Thus much computational time can be saved. In the new Newton MFEM, we first solve the equation for the temperature, then solve a Navier–Stokes problem by Newton iterative method. While in the two-level method, we solve the decoupled conduction–convection problem as same as in the one-level method using a coarse grid firstly, then seek a fine grid solution by solving a linearized problem on a fine grid. Stability analysis is performed and error estimates of the methods are derived, which show that our methods are stable and have a good precision. Numerical experiments are also given, which confirm the theoretical analysis and demonstrate the efficiency of the new methods. [ABSTRACT FROM AUTHOR]

In this paper, we develop an online generalized multiscale approximation of the multipoint flux mixed finite element method (MFMFE) for Darcy flow in highly heterogeneous porous media, which can handle full tensor permeability fields and unstructured grids with local velocity elimination. Here, for illustration of the proposed method, we will mainly consider the situation that the porous medium is filled with fractures, which usually results in unstructured grids, and the extension to the situation that the permeability is represented as a full tensor is straightforward. From the fine-grid discretization by the MFMFE method, we derive the symmetric and positive definite discrete bilinear form for both the matrix and fracture pressure, and thereby obtain the corresponding discrete weak formulation that only related to pressure. In the offline stage, we compute offline basis functions which contain the important local multiscale information of each coarse-grid block to form the initial multiscale space. In the online stage, we construct and add online basis functions to enrich the multiscale space and consequently improve the accuracy of the multiscale solution. Each offline basis function and each online basis function contains multiscale information both for matrix and fracture. We give the theoretical analysis for the convergence of the online enrichment, which shows that more sufficient initial basis functions lead to faster convergence rates. A series of numerical examples that either the permeability is a full tensor or the porous medium is filled with fractures are presented to show the performance of the multiscale method. • An online generalized multiscale approximation of the MFMFE method is proposed. • The proposed method can handle full tensor permeabilities and unstructured grids. • The proposed method can simulate Darcy flow in fractured porous medium. • The discrete bilinear form for pressure is symmetric and positive definite. [ABSTRACT FROM AUTHOR]

Various disturbances do exist in the image taking process of scanning transmission electron microscopes (STEM), which seriously reduces the resolution and accuracy of STEM images. In this paper, a deep understanding of the scanning distortion influence on the real and reciprocal spaces of STEM images is achieved via theoretical modeling and simulation. A scanning distortion correction algorithm is further developed based on two images scanned along perpendicular directions, which is able to effectively correct scanning distortion induced deviations and significantly increase the signal to noise ratio of STEM images. [ABSTRACT FROM AUTHOR]

Abstract: Indentation stresses in single- and multi-layer delaminated thin films made of elastic–perfectly plastic materials in microwedge indentation delamination tests are analyzed via finite element calculations with different wedge angles and other geometrical and mechanical parameters. Based on the formula for a single-layer thin film under indentation loading [Zhao et al. J Mater Res 2009;24:1943] and by introducing the equivalent material parameters, we developed simple analytical formulae for the loading indentation stress (as well as the energy release rate) in each layer of the multi-layer thin film, in terms of the residual stress, elastic modulus, Poisson’s ratio, yielding strength, and thickness of each layer. Our analytical solution is validated by the finite element calculations and should be useful to thin-film delamination tests. [Copyright &y& Elsevier]