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Balanced a posteriori error estimates for finite-volume type discretizations of convection-dominated elliptic problems

Ausgewogene a posteriori Fehlerabschätzungen für Finite-Volumen-Diskretisierungen von konvektionsdominierten elliptischen Problemen

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Abstract

The paper describes computable local a posteriori error estimates for the numerical solution of convection-dominated boundary-value problems. Being applied to singularly perturbed elliptic equations, the obtained estimates are uniform w.r.t. the small parameter. Moreover, if quadrature errors are neglected the numerical approximation of the theoretical error bounds preserves the relation signs in the estimates.

Zusammefassung

Die Arbeit beschreibt berechenbare lokale a posteriori Fehlerabschätzungen für die numerischen Lösung konvektionsdominanter Randwertaufgaben. Bei Anwendung auf singulär gestörte Gleichungen erweisen sich die gewonnenen Abschätzungen als gleichmäßig bzgl. des kleinen Parameters. Wird ferner der Quadraturfehler vernachlässigt, konserviert die numerische Approximation der theoretischen Schranken die Relationszeichen in den Abschätzungen.

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  1. Institut für Angewandte Mathematik, Universität Erlangen-Nürnberg, Martensstrasse 3, D-91058, Erlangen, Federal Republic of Germany

    L. Angermann

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  1. L. Angermann
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Angermann, L. Balanced a posteriori error estimates for finite-volume type discretizations of convection-dominated elliptic problems. Computing 55, 305–323 (1995). https://doi.org/10.1007/BF02238485

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  • DOI: https://doi.org/10.1007/BF02238485

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