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Abstract: In this paper, we consider the elastomechanical problems of a honeycomb structure of composite materials. A multiscale finite element method and the postprocessing technique with high accuracy are presented. We will derive the proofs of all theoretical results. Finally, some numerical tests validate the theoretical results of this paper. [Copyright &y& Elsevier]

Abstract: We present an adaptive sparse grid algorithm for the solution of the Black–Scholes equation for option pricing, using the finite element method. Sparse grids enable us to deal with higher-dimensional problems better than full grids. In contrast to common approaches that are based on the combination technique, which combines different solutions on anisotropic coarse full grids, the direct sparse grid approach allows for local adaptive refinement. When dealing with non-smooth payoff functions, this reduces the computational effort significantly. In this paper, we introduce the spatially adaptive discretization of the Black–Scholes equation with sparse grids and describe the algorithmic structure of the numerical solver. We present several strategies for adaptive refinement, evaluate them for different dimensionalities, and demonstrate their performance showing numerical results. [Copyright &y& Elsevier]

Abstract: The problem of finding the least change adjustment to a stiffness matrix modeled by finite element method is considered in this paper. Desired stiffness matrix properties such as symmetry, sparsity, positive semidefiniteness, and satisfaction of the characteristic equation are imposed as side constraints of the constructed optimal matrix approximation for updating the stiffness matrix, which matches measured data better. The dual problems of the original constrained minimization are presented and solved by subgradient algorithms with different line search strategies. Some numerical results are included to illustrate the performance and application of the proposed methods. [Copyright &y& Elsevier]

Abstract: In this paper, we analyze a FEM and two-grid FEM decoupling algorithms for elliptic problems on disjoint domains. First, we study the rate of convergence of the FEM and, in particular, we obtain a superconvergence result. Then with proposed algorithms, the solution of the multi-component domain problem (simple example — two disjoint rectangles) on a fine grid is reduced to the solution of the original problem on a much coarser grid together with solution of several problems (each on a single-component domain) on fine meshes. The advantage is the computational cost although the resulting solution still achieves asymptotically optimal accuracy. Numerical experiments demonstrate the efficiency of the algorithms. [Copyright &y& Elsevier]

Abstract: In this paper we revisit a quasi-static contact problem of a thermoviscoelastic beam between two rigid obstacles which was recently studied in . The variational problem leads to a coupled system, composed of an elliptic variational inequality for the vertical displacement and a linear variational equation for the temperature field. Then, its numerical resolution is considered, based on the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. Error estimates are proved from which, under adequate regularity conditions, the linear convergence is derived. Finally, some numerical simulations are presented to show the accuracy of the algorithm and the behavior of the solution. [Copyright &y& Elsevier]

Abstract: In the course of the numerical approximation of mathematical models there is often a need to solve a system of linear equations with a tridiagonal or a block-tridiagonal matrices. Usually it is efficient to solve these systems using a special algorithm (tridiagonal matrix algorithm or TDMA) which takes advantage of the structure. The main result of this work is to formulate a sufficient condition for the numerical method to preserve the non-negativity for the special algorithm for structured meshes. We show that a different condition can be obtained for such cases where there is no way to fulfill this condition. Moreover, as an example, the numerical solution of the two-dimensional heat conduction equation on a rectangular domain is investigated by applying Dirichlet boundary condition and Neumann boundary condition on different parts of the boundary of the domain. For space discretization, we apply the linear finite element method, and for time discretization, the well-known -method. The theoretical results of the paper are verified by several numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we construct a second order algorithm based on the semi-implicit spectral deferred correction method for the non-stationary coupled Navier–Stokes/Darcy equations with the Beavers–Joseph–Saffman's interface condition. We present a complete theoretical analysis to prove that this algorithm is stable and possesses second order accuracy in time. Numerical examples confirm the convergence rate and the effectiveness of our algorithm. [ABSTRACT FROM AUTHOR]