A modified weak Galerkin finite element methods for convectiondiffusion problems in 2D
In this paper, we develop a modified weak Galerkin finite element method on arbitrary grids for convectiondiffusion problems in two dimensions based on our previous work (Wang et al., J Comput Appl Math 271, 319327, 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 \(H^1\) norm and the standard \(L^2\) norm. Numerical results are presented to demonstrate the robustness, reliability, and accuracy of the MWG-FEM.
convectiondiffusion weak gradient weak divergence error estimate wg 65m15 65m60