L2- OPTIMAL ORDER ERROR FOR TWO-DIMENSIONAL COUPLED BURGERS' EQUATIONS BY WEAK GALERKIN FINITE ELEMENT METHOD

L2- OPTIMAL ORDER ERROR FOR TWO-DIMENSIONAL COUPLED BURGERS' EQUATIONS BY WEAK GALERKIN FINITE ELEMENT METHOD

A. J. Hussein, H. A. Kashkool

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Abstract

In this paper, we present a continuous time and discrete time weak Galerkin  nite 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  nite element schemes. The Nu- merical examples are in good agreement with the theoretical analysis and polynomial mixture fPk(K); Pk-1(@K); [Pk-1(K)]2g.

Keywords

Weak Galerkin Finite Element Method (WG-FEM), Burgers' Equations, Op- timal order error.