The Upwind Finite Volume Element Method for Two-Dimensional Burgers Equation

Abstract

A finite volume element method for approximating the solution to two-dimensional Burgers equation is presented. Upwind technique is applied to handle the nonlinear convection term. We present the semi-discrete scheme and fully discrete scheme, respectively. We show that the schemes are convergent to order one in space in $L^{\mathrm{2}}$-norm. Numerical experiment is presented finally to validate the theoretical analysis.