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The paper presents a new method for the numerical solution of transient linear heat conduction problems. In the proposed method, the transient linear heat conduction equation is first integrated with respect to time over subsequent intervals. Then the resulting set of elliptic equations is discretized in space according to a finite-element procedure. The method is unconditionally stable. At the end of the paper, the effectiveness of the proposed method is assessed through some numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, a modified characteristics finite element method for the time dependent Navier-Stokes/Darcy problem with the Beavers-Joseph-Saffman interface condition is presented. In this method, the Navier-Stokes/Darcy equation is decoupled into two equations, one is the Navier-Stokes equation, the other is the Darcy equation, and the Navier-Stokes equation is solved by the modified characteristics finite element method. The theory analysis shows that this method has a good convergence property. In order to show the effect of our method, some numerical results was presented. The numerical results show that this method is highly efficient. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This paper presents a complete formulation for three-dimensional hydrodynamic analysis of floating flexible structures subjected to surface regular waves, as well as other excitation forces, by employing a direct tight coupling method. The continuum mechanics-based finite element method is employed to model floating structures with arbitrary geometries, which can account for the geometric nonlinearities and initial stress effects that result from the hydrostatic analysis, whereas the boundary element method is used for the fluid via total potential formulation. The simplicity and generality of the present formulation are revealed as compared with the conventional formulation. Numerical examples demonstrate the general capability of the formulation proposed. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, we replace the asymptotic enrichments around the crack tip in the extended finite element method (XFEM) with the semi-analytical solution obtained by the scaled boundary finite element method (SBFEM). The proposed method does not require special numerical integration technique to compute the stiffness matrix, and it improves the capability of the XFEM to model cracks in homogeneous and/or heterogeneous materials without a priori knowledge of the asymptotic solutions. A Heaviside enrichment is used to represent the jump across the discontinuity surface. We call the method as the extended SBFEM. Numerical results presented for a few benchmark problems in the context of linear elastic fracture mechanics show that the proposed method yields accurate results with improved condition number. A simple code is annexed to compute the terms in the stiffness matrix, which can easily be integrated in any existing FEM/XFEM code. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY The most difficult aspect of modelling discontinuity on complicated domains is the mesh. In the extended finite element method (XFEM), the FE mesh need not conform to the internal boundaries. In the intrinsic XFEM, no additional unknowns are introduced at the nodes. Some of these discontinuities such as cracks, voids were developed in earlier papers. In the current work, the FE mesh is allowed to be independent of the rigid line (fixed DOFs path). Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We show that if the sum of the resistances of an electrical network N is finite, then there is a unique electrical current in N, provided that we do not allow, in a sense made precise in the paper, any flow to escape to infinity. [ABSTRACT FROM PUBLISHER]

An algorithm combining the numerical execution in time of implicit and explicit methods of solution is presented in this paper. The algorithm swaps between both methods as required for the analysis. The whole mesh is solved for an unique method at once, i.e. there are no partitions of the mesh for separate implicit or explicit treatment of the solution. The combination is in-time, in such a manner that if the implicit method starts diverging the explicit one is initiated by appropriate conditions of transition. The formulation is presented first and its implementation is validated by the analysis of a key numerical example. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We consider strategies to construct optimal order two- and multilevel hierarchical preconditioners for linear systems as arising from the finite element discretization of self-adjoint second order elliptic problems using non-conforming Crouzeix–Raviart linear elements. In this paper we utilize the hierarchical decompositions, derived in a previous work by the same authors (Numerical Linear Algebra with Applications 2004; 11:309–326) and provide a further analysis of these decompositions in order to assure robustness with respect to anisotropy. Finally, we show how to construct both multiplicative and additive versions of the algebraic multilevel iteration preconditioners and show robustness and optimal order convergence estimates. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper contains a final identification theorem for the ‘generic’ $K^*$-groups of finite Morley rank. [ABSTRACT FROM AUTHOR]

Utilizing systematically differential geometry the paper describes a method which substantially improves results obtained by Yuan et al. (1994), though the same technique is used in both articles. An 8-node isoparametric element with curved boundaries is analysed as an object of differential geometry. Inverse transformations between normal (geodesic) co-ordinates and natural (isoparametric) co-ordinates are derived in terms of a Taylor series which is convergent and does not need many terms to give an excellent approximation of the element shape with four curved sides. The concept of local normal co-ordinates results in the definition of distortion measures of a plane element. It is shown, by exploring the theory of geodesic curves, that the distortion parameters of a chord quadrilateral, spanned on the corner nodes of the 8-node element with curved boundaries, are the basic distortion measures for this 8-node element. Thus, significant reduction of the number of these parameters, from 12 to 4, from previous works is obtained. For the purpose of the finite element method, which is very sensitive to a shape of quadrilateral elements, only basic deviation measures from a regular form of a plane element are of interest. The distortion measures due to curvatures of sides seem to be of secondary significance in the analysis if straight sides of the chord quadrilateral and curved boundaries are isomorphic. The mathematical analysis used is quite general and relies strongly on differential geometry. The results are independent of co-ordinate systems. The meaning of element distortion measures is suggested. This analysis can be extended to curved surfaces in R3. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper the superconvergence property of isoparametric bilinear finite elements is considered. A new superconvergence recovery method for isoparametric bilinear finite elements is discovered on the four vertices and the four midpoints of the edges of the elements for piecewise strongly regular quadrilateral subdivisions. [ABSTRACT FROM AUTHOR]

In the paper a mathematical formulation for embedding reinforcements in 3D brick concrete elements is presented. The computational aspects and the implementation process of the model have been discussed. The proposed algorithm may be implemented in 3D finite element programs for stress analysis of reinforced concrete structures. [ABSTRACT FROM AUTHOR]

The paper presents a formulation and analysis of three and four step least squares algorithms for first order IVPs. The three step algorithm is derived using cubic Lagrangian interpolation, and is found to be third order accurate but only conditionally stable. Fourth order Lagrangian interpolation is used to obtain a four step least squares scheme which is Ao-stable but inconsistent. [ABSTRACT FROM AUTHOR]

In the paper a computation code based on the finite-element method for temperature evolutions in composite elements with internal cavities is presented. It is suitable for the analysis of various thermal problems encountered in mechanical and civil engineering such as fire risk assessment. It is based on a plane isoparametric triangular element with six nodes allowing the modeling of curved boundaries. In order to analyze composite steel-concrete elements and to take into account the non-linearities coming from the temperature-dependent material properties and from the boundary conditions, an implicit integration scheme is used. Another advantage of the program is the possibility of describing internal cavities with convection and radiation exchanges. In order to show the capacity of the program two examples are presented. Comparisons have been made with experimental and other numerical results, exhibiting very good agreement. [ABSTRACT FROM AUTHOR]

The calculation of the pressure cycle is of crucial importance for the successful development of a thin sheet superplastic forming process. The pressure cycle must be such that the forming time is minimized while maintaining a strain rate that maximizes the strain-rate sensitivity parameter, in order to reduce the propensity of the material to undergo localized necking. One way of dealing with this problem is to control the pressure by constraining the maximum equivalent strain rate. This paper presents a general numerical algorithm for achieving such control, in conjunction with a finite element analysis of the forming process. Three examples are given of strain-rate controlled pressure cycles for the forming of a plane-strain strip. [ABSTRACT FROM AUTHOR]

Commonly used geometric idealizations in finite element analyses introduce errors which required either a large number of degrees of freedom or the use of special procedures to correct. In this paper the effect of geometric idealizations on computer data is examined through the example of a spherical shell with an edge ring. This example demonstrates that in typical structural problems it is better to avoid the use of sharp reentrant corners than to compensate for them by mesh refinement. The effect of different mapping techniques is also examined. [ABSTRACT FROM AUTHOR]

For transient thermal problems, discretizing in space by the finite element method yields a system of first-order ordinary differential equations which can be integrated in time by a finite difference based predictor-multicorrector scheme. At each time level the temperature field is obtained by solving a set of algebraic equations. In this paper the multigrid method is adopted for transient thermal problems. In order to model accurately the geometry of practical problems with various material properties, and to use the predictor-corrector scheme for the nonlinear transient analysis, the generalized multigrid approach, similar to that proposed in Reference 1, is employed. Some examples are included to illustrate the performance of this approach for nonlinear transient problems. [ABSTRACT FROM AUTHOR]

Recently. a new class of error indicators and estimators for the finite element method has been introduced which is particularly easy to implement into existing finite element codes. This paper proves that the new indicators are equivalent to those analyzed earlier by Babuska, thus showing that the rigorous mathematical results for the well-known jump indicator apply also for the new ones. [ABSTRACT FROM AUTHOR]

A finite-element implementation for the analysis of propagation constants and fields in a guiding structure is presented in this paper. The solution explicitly takes into account the field divergence on the edges of the internal wedges by exploiting substitutive divergent bases. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 44: 327–328, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20624 [ABSTRACT FROM AUTHOR]