Multiscale Element-Free Galerkin Method with Penalty for 2D Burgers’ Equation

In this paper, a new numerical method which is based on the coupling between multiscale method and meshless method with penalty is developed for 2D Burgers’ equation. The advantage of meshless method over the finite element method (FEM) is that remeshing process is not required. This is because the meshless method approximation is constructed entirely in terms of a set of nodes. Since the moving least squares (MLS) shape function does not satisfy the Kronecker delta property, so penalty method is adopted to enforce the essential boundary conditions in this paper. In order to obtain the fine scale approximation, the local enrichment basis is applied. The local enrichment basis may adopt the polynomial basis functions or any other analytical basis functions. Here, the polynomial basis functions are chosen as local enrichment basis. This multiscale meshless method with penalty will provide a more accurate result especially in the critical region which requires higher accuracy. It is believed that this proposed method is an attractive approach for solving more general problems which involve large deformation.