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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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A posteriori error estimates for upwind finite volume schemes for nonlinear conservation laws in multi dimensions
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by Dietmar Kröner and Mario Ohlberger PDF
Math. Comp. 69 (2000), 25-39 Request permission

Abstract:

In this paper we shall derive a posteriori error estimates in the $L^1$-norm for upwind finite volume schemes for the discretization of nonlinear conservation laws on unstructured grids in multi dimensions. This result is mainly based on some fundamental a priori error estimates published in a recent paper by C. Chainais-Hillairet. The theoretical results are confirmed by numerical experiments.
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Additional Information
  • Dietmar Kröner
  • Affiliation: Institut für Angewandte Mathematik, Universität Freiburg, Herrmann-Herder-Str. 10, 79104 Freiburg, Germany
  • Email: dietmar@mathematik.uni-freiburg.de, mario@mathematik.uni-freiburg.de
  • Mario Ohlberger
  • Affiliation: Institut für Angewandte Mathematik, Universität Freiburg, Herrmann-Herder-Str. 10, 79104 Freiburg, Germany
  • Received by editor(s): February 5, 1998
  • Published electronically: August 18, 1999
  • © Copyright 1999 American Mathematical Society
  • Journal: Math. Comp. 69 (2000), 25-39
  • MSC (1991): Primary 65M15, 35L65, 76M25
  • DOI: https://doi.org/10.1090/S0025-5718-99-01158-8
  • MathSciNet review: 1659843