Numerische Mathematik

, Volume 88, Issue 3, pp 459–484 | Cite as

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

  • Bernard Haasdonk
  • Dietmar Kröner
  • Christian Rohde
Original article

Summary.

Based on Nessyahu and Tadmor's nonoscillatory central difference schemes for one-dimensional hyperbolic conservation laws [16], for higher dimensions several finite volume extensions and numerical results on structured and unstructured grids have been presented. The experiments show the wide applicability of these multidimensional schemes. The theoretical arguments which support this are some maximum-principles and a convergence proof in the scalar linear case. 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. 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 nonlinear scalar hyperbolic conservation law.

Mathematics Subject Classification (1991): 65M12 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Bernard Haasdonk
    • 1
  • Dietmar Kröner
    • 1
  • Christian Rohde
    • 1
  1. 1.Institut für Angewandte Mathematik, Herrmann-Herder-Strasse 10, 79104 Freiburg, Germany; e-mail: {haasdonk,chris,dietmar}@mathematik.uni-freiburg.de DE

Personalised recommendations