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A Posteriori Error Estimates and Adaptive Methods for Hyperbolic and Convection Dominated Parabolic Conservation Laws

In: Trends in Nonlinear Analysis

Author

Listed:
  • Dietmar Kröner

    (Universität Freiburg, Institut für Angewandte Mathematik)

  • Marc Küther

    (Universität Freiburg, Institut für Angewandte Mathematik)

  • Mario Ohlberger

    (Universität Freiburg, Institut für Angewandte Mathematik)

  • Christian Rohde

    (Universität Freiburg, Institut für Angewandte Mathematik)

Abstract

In this contribution we will give a survey on rigorous a posteriori error estimates and adaptive methods for finite volume approximations of hyperbolic and convection dominated parabolic conservation laws. Scalar problems are considered as well as weakly coupled systems where the coupling is only due to lower order terms. In the context of scalar hyperbolic conservation laws error estimates are obtained for cell centered finite volume schemes and for the staggered Lax—Friedrichs scheme in multi dimensions. In the case of weakly coupled convection dominated parabolic equations we get a posteriori error estimates for a vertex centered finite volume scheme which are uniform in the lower bound of the diffusion. Numerical experiments underline the applicability of the theoretical results in adaptive computations.

Suggested Citation

  • Dietmar Kröner & Marc Küther & Mario Ohlberger & Christian Rohde, 2003. "A Posteriori Error Estimates and Adaptive Methods for Hyperbolic and Convection Dominated Parabolic Conservation Laws," Springer Books, in: Markus Kirkilionis & Susanne Krömker & Rolf Rannacher & Friedrich Tomi (ed.), Trends in Nonlinear Analysis, chapter 7, pages 289-306, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-05281-5_7
    DOI: 10.1007/978-3-662-05281-5_7
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