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Generalization of the Nessyahu-Tadmor scheme for hyperbolic equations in two space dimensions. (Généralisation du schéma de Nessyahu-Tadmor pour une équation hyperbolique à deux dimensions d’espace.) (French. English summary) Zbl 0831.65091
Summary: The scheme of H. Nessyahu and E. Tadmor [J. Comput. Phys. 87, No. 2, 408-463 (1990; Zbl 0697.65068)] is a van Leer type scheme built on the Lax-Friedrichs scheme. It is defined for a one-dimensional hyperbolic problem and the convergence to the entropic solution is proved in the case of a single equation. In this note an extension to a two-dimensional scalar equation with an unstructured mesh is proposed.

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