Mixed Covolume Method For Two-Dimensional Burgers Equation On Triangular Grids

We consider the following two-dimensional Burgers equationIn the first chapter, we propose mixed covolume method for two-dimensional Burgers equation on triangular grids. This method has the characteristics of high precision and simple caculation. In this chapter, the semi-discrete and fully discrete schemes are defined, and the lowest order Raviart-Thomas mixed element spaces on triangular mesh are used. By conducting the numerical analysis, we obtain the error estimates of L2-norm about the functions.Then, we present the numerical example of the problem. We run a numerical simulation which got numerical solutions respectively considering different values of ζ. At last we got the genuine solution of function u, v and the error order of the discrete solution. Thus, we verified the effectiveness of the mixed covolume method by the simulation which proved that the convergence order is matched with theoretical analysis.