Discontinuous Volume Method For Two-Dimensional Burgers Equation

In this paper, we consider the following coupled two-dimensional Burgers equation,where ?(?)R~2 is a bounded spatial domain.At first, we propose the upwind discontinuous finite volume element method for two-dimensional Burgers equation on triangular grids. The semi-discrete and fully discrete schemes are presented. Through detailed theoretical analysis, we obtain the error estimates of L~2-norm about the unknown functions. By numerical examples,we show the effectiveness of this method.Then, we propose the discontinuous mixed covolume element method for twodimensional Burgers equation on triangular grids. The semi-discrete and fully discrete schemes are presented. Through detailed theoretical analysis, we obtain the error estimates of L~2-norm about the unknown functions and energy norm about the flux.