THE ERROR CONVERGENCE OF THE WEAK GALERKIN METHOD FOR TWO-DIMENSIONAL NON-LINEAR CONVECTION-DIFFUSION PROBLEM

Abstract

. This paper presents the fully-discrete scheme for the solution of two-dimensional non-linear convection diffusion equations by using the Crank-Nicolson-Weak Galerkin finite element methods. We introduce and analyze stability. The error estimate and an optimal order of ( L 2 and H 1 )-norm are proved. We confirm the theoretical results with some numerical examples.