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PSI Solution of Convection-Diffusion Equations with Data in L1

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • J. Casado-Díaz

    (Universidad de Sevilla, Dpto. Ecuaciones Diferenciales y Análisis Numérico)

  • T. Chacón Rebollo

    (Universidad de Sevilla, Dpto. Ecuaciones Diferenciales y Análisis Numérico)

  • V. Girault

    (UPMC, Univ Paris 06, UMR 7598, Laboratoire Jacques Louis Lions)

  • M. Gómez Mármol

    (Universidad de Sevilla, Dpto. Ecuaciones Diferenciales y Análisis Numérico)

  • F. Murat

    (UPMC, Univ Paris 06, UMR 7598, Laboratoire Jacques Louis Lions)

Abstract

This paper is devoted to the analysis of finite element approximations of convection-diffusion equations with data in L1. We discretize the convection operator by the PSI (Positive Streamwise Implicit) scheme, and the diffusion operator by the standard Galerkin method, using conforming P1 finite elements. We give the main idea in the proof of convergence of the approximations to the unique renormalized solution in $$W^{1,q}(\Omega),1\leq q

Suggested Citation

  • J. Casado-Díaz & T. Chacón Rebollo & V. Girault & M. Gómez Mármol & F. Murat, 2008. "PSI Solution of Convection-Diffusion Equations with Data in L1," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 233-240, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_27
    DOI: 10.1007/978-3-540-69777-0_27
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