A weak Galerkin finite element method for two-dimensional coupled burgers’ equation by using polynomials of order (k, k – 1, k – 1)

Abstract

In this paper, we suggest a Weak Galerkin Finite Element Method (WGFEM) for solving two dimensional coupled Burgers’ equations with a stabilization term and spicail trilinear form for nonlinear term . We introduce two numerical scheme, the first continuous time weak Galerkin finite element method (CTWGFEM) and the second discrete time weak Galerkin finite element method (DTWGFEM), As well, we use a polynomial mixtue that reduces the number of unknowns in the numerical scheme with no change in the preciseness of the numerical approximation [1]. For clarification purpose, We use polynomial space of degree on each element, polynomial space of degree on the edge and polynomial space of degree for space of weak gradient operator of each element. Convergence order estimate in trip-barnorm and norm it was received. Theoretical proofs matched with numerical results by test problem.