On the Accuracy of a Numerical Method for Two-dimensional Scalar Conservation Laws Based on Dimensional Splitting and Front Tracking

A rigorous proof of an error estimate for a numerical method for two-dimensional scalar conservation laws is presented. The numerical method under consideration is based on the use of dimensional splitting and front tracking to solve the one-dimensional equations. It is shown that the error is bounded by C(((t) 1=2 + ((x) 1=2 +), where x is the space step, t is the time step, is the parameter measuring the polygonal approximation of the ux functions, and C is a nite constant independent of the discretization parameters. Furthermore, we implement the method on a computer to supplement the theoretical results with numerical examples.