标题：A modified weak Galerkin finite element methods for convection–diffusion problems in 2D
作者：Gao, Fuzheng ;Wang, Xiaoshen ;Mu, Lin
作者机构：[Gao, Fuzheng ] School of Mathematics, Shandong University, Jinan; Shandong; 250100, China;[Wang, Xiaoshen ] Department of Mathematics, University of 更多
来源：Journal of Applied Mathematics and Computing
摘要：In this paper, we develop a modified weak Galerkin finite element method on arbitrary grids for convection–diffusion problems in two dimensions based on our previous work (Wang et al., J Comput Appl Math 271, 319–327, 2014), in which we only considered second order Poisson equations and thus only introduced a modified weak gradient operator. This method, called MWG-FEM, is based on a modified weak gradient operator and weak divergence operator which is put forward in this paper. Optimal order error estimates are established for the corresponding MWG-FEM approximations in both a discrete H1norm and the standard L2norm. Numerical results are presented to demonstrate the robustness, reliability, and accuracy of the MWG-FEM.
© 2014, Korean Society for Computational and Applied Mathematics.