Convergence of a staggered Lax-Friedrichs scheme for nonlinear conservation laws on unstructured two-dimensional grids

Based on Nessyahu and Tadmor's nonoscillatory central difference schemes fo r one-dimensional hyperbolic conservation laws [16], for higher dimensions several finite volume extensions and numerical results on structured and un structured grids have been presented. The experiments show the wide applica bility of these multidimensional schemes. The theoretical arguments which s upport this are some maximum-principles and a convergence proof in the scal ar linear case. A general proof of convergence, as obtained for the origina l one-dimensional NT-schemes, does not exist for any of the extensions to m ultidimensional nonlinear problems. For the finite volume extension on two- dimensional unstructured grids introduced by Arminjon and Viallon [3,4] we present a proof of convergence for the first order scheme in case of a nonl inear scalar hyperbolic conservation law.