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Finite volume methods with local refinement for convection-diffusion problems

Finite Volumen-Methoden mit lokaler Verfeinerung für Konvektions-Diffusions-Probleme

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Abstract

Based on approximation of the balance relation for convection-diffusion problems, finite difference schemes on rectangular locally refined grids are derived and studied. A priori estimates and error bounds in discreteH 1-norm are provided. Numerical examples demonstrating the accuracy of the schemes for a variety of model convection-diffusion problems are presented and discussed.

Zusammenfassung

Auf der Grundlage der Gleichgewichtsrelation für Konvektions-Diffusions-Probleme werden endliche Differenzschemata auf rechteckigen lokal verfeinerten Gittern hergeleitet und untersucht. Weiterhin werden a-priori-Abschätzungen und Fehlerschranken in der diskretenH 1-Norm angegeben. Numerische Beispiele zeigen die Genauigkeit der Schemata für verschiedene Modelle von Konvektions-Diffusions-Problemen.

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, 7784303368, College Station, TX, U.S.A.

    R. D. Lararov &  I. D. Mishev

  2. Center for Computer Science and Technology, Bulgarian Academy of Sciences, Acad. G. Bontchev Street Block 25A, 113, Sofia, Bulgaria

    P. S. Vassilevski

Authors
  1. R. D. Lararov
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  2. I. D. Mishev
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  3. P. S. Vassilevski
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Additional information

This research of the second and third authors was partially supported by the Department of Energy under contract DE-FG03-87ER25037, by the Army Research Office under contract ARO DAAL 03-91-G-150 and by the National Science Foundation under grant NSF ASC-92-01266. The third author was also supported in part by the National Science Foundation under grant NSF-INT-92-20287.

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Lararov, R.D., Mishev, I.D. & Vassilevski, P.S. Finite volume methods with local refinement for convection-diffusion problems. Computing 53, 33–57 (1994). https://doi.org/10.1007/BF02262107

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