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An explicit method for convection-diffusion equations

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Abstract

An explicit scheme for time-dependent convection-diffusion problems is presented. It is shown that convenient bounds for the time step value ensureL ∞ stability, in both space and time, for piecewise linear finite element discretizations in any space dimension. Convergence results in the same sense are also demonstrated under certain conditions. Numerical results certify the good performance of the scheme.

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Authors and Affiliations

  1. Institut Jean Le Rond d’Alembert, Université Paris 6, France

    Vitoriano Ruas

  2. Visiting Researcher at Departamento de Análise, Universidade Federal Fluminense, Rio de Janeiro, Brazil

    Vitoriano Ruas

  3. Departamento de Engenharia Mecânica, Universidade de Brasília, Brasília, Brazil

    Antonio Brasil

  4. Departamento de Análise, Universidade Federal Fluminense, Rio de Janeiro, Brazil

    Paulo Trales

Authors
  1. Vitoriano Ruas
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  2. Antonio Brasil
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  3. Paulo Trales
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Corresponding author

Correspondence to Vitoriano Ruas.

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Dedicated to the memory of Francisco Ruas Santos.

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Ruas, V., Brasil, A. & Trales, P. An explicit method for convection-diffusion equations. Japan J. Indust. Appl. Math. 26, 65 (2009). https://doi.org/10.1007/BF03167546

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  • DOI: https://doi.org/10.1007/BF03167546

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