Abstract
In this paper we consider the LDA (Low Diffusion Advection) scheme for solving conservation laws in two space dimensions as it was published in [1],[2], [5]. For a special grid and a special nonlinearity we will show by constructing a counterexample that there is no convergence of the numerical solution to the exact solution.
The example is constructed in such a way that the exact solution as well as the numerical solution are computed explicitly.