Error analysis of weak Galerkin finite element methods for time-dependent convection-diffusion equations

摘要

In this paper, a fully discrete weak Galerkin (WG) finite element method is presented for solving time-dependent convection-dominated diffusion equations with convection term in non-conservation form. WG method and Crank-Nicolson scheme are used for spatial and temporal discretization, respectively. Stability and error analysis are established on polygonal mesh. Numerical examples are presented to verify our theoretical findings and show the efficiency of the method. (C) 2018 IMACS. Published by Elsevier B.V. All rights reserved.