L²- Optimal order error for two-dimensional coupled burgers’ equations by weak Galerkin finite element method

Abstract

In this paper, we present a continuous time and discrete time weak Galerkin finite element schemes for solving non linear two Dimensional coupled Burgers’ equations with a stabilization term. We use special weak form (trilinear form) for nonlinear term. The optimal order error in L²- norm is obtained based on dual argument technique for both continuous time and discrete time weak Galerkin finite element schemes. The Numerical examples are in good agreement with the theoretical analysis and polynomial mixture {Pk(K), Pk−1(∂K), [Pk−1(K)]2}.