Higher-order multiscale finite element method for linear elasticity equations with oscillating coefficients

Abstract

In this paper, we study higher-order Multiscale Finite Element Method (MsFEM) to solve linear elasticity equations with oscillating coefficients. Compared to the Finite Element Method (FEM), MsFEM can obtain the characteristics of fine scale in coarse mesh by using carefully designed multiscale basis functions. By using higher-order basis functions, better accuracy can be achieved. To further improve accuracy, several techniques are considered: oversampling methods and oscillatory boundary conditions (OBCs) are used to prevent the influence of boundary conditions on the construction of multiscale basis functions; the Petrov-Galerkin method, with the trial functions being multiscale basis functions and the test functions being polynomial functions. Numerical examples are presented to demonstrate the efficiency of the proposed methods.