A modified weak Galerkin finite element method for the linear elasticity problem in mixed form

Abstract

In this paper, we present and analyze the modified weak Galerkin (MWG) finite element method to the linear elasticity problem in a mixed form. Comparing with weak Galerkin (WG) finite element method, the structure of modified weak Galerkin (MWG) finite element method is especial. The main idea of MWG finite element method for elasticity problem is to express to boundary stress tensor defined on the partition boundary in terms of the average of the interior stress tensor defined inside partition elements. This can substantially reduce the degrees of freedom of the linear system. The well-posedness of the solution and inf–sup condition are investigated in this paper. We obtain the optimal error estimates in both energy norm and L2 norm. Finally, some numerical experiments are exhibited to illustrate the efficiency and accuracy of the modified weak Galerkin finite element method.