Error Estimate for Two-Dimensional Coupled Burgers’ Equations By Weak Galerkin Finite Element Method

Abstract

Abstract A weak Galerkin finite element method (WG-FEM) can be considered a general finite element methods for solving partial differential equations (PDEs) by approximating the differential operators as distributions in weak forms. A weak Galerkin finite element method is used in this work for solving two Dimensional Burgers’ equations in lowest order Raviart-Thomas element RT 0 with polynomails of constant basis. Both the continuous and discrete time WG-FEM are analysed.The optimal order estimates in H 2-error and L 2 –error are obtained. Numerical results are applied to clarify the theoretical analysis.