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Convergence of a staggered Lax-Friedrichs scheme for nonlinear conservation laws on unstructured two-dimensional grids. (English) Zbl 1001.65102
The purpose of this paper is to study convergence of the most simple Nessyahu-Tadmor (NT) scheme, the staggered Lax-Friedrichs scheme, on unstructured two-dimensional grids. A general proof of convergence, as obtained for the original one-dimensional NT-schemes, does not exist for any of the extensions to multidimensional nonlinear problems. The authors present a proof of convergence for the first-order scheme (in case of nonlinear scalar hyperbolic conservation laws) on two-dimensional unstructured grids introduced by P. Arminjon and M. C. Viallon [C. R. Acad. Sci., Paris, Sér. I 320, No. 1, 85-88 (1995; Zbl 0831.65091); Proceedings of the 6th Int. Symposium on Comp. Fluid Dynamics, Lake Tahoe 4, 7-14 (1995)].

MSC:
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
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