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Galerkin collocation for an improved boundary element method for a plane mixed boundary value problem

Galerkin-Kollokation für eine verbesserte Randelement-Methode für ein ebenes gemischtes Randwertproblem

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Abstract

We present the numerical implementation of a boundary element approximation for the plane mixed boundary value problem of the Laplacian. The performed Galerkin procedure is based on the direct boundary integral method. Its accuracy is improved by using appropriate singularity functions as additional test and trial functions besides quadratic splines. We analize the consistency error of the used numerical integrations and present asymptotic error estimates for the fully discretized numerical scheme which are of the same optimal orders as the Galerkin errors.

Zusammenfassung

Wir beschreiben die numerische Durchführung einer Randelement-Approximation für das ebene gemischte Randwertproblem für harmonische Funktionen. Grundlage unseres Galerkin-Verfahrens ist die direkte Randintegralmethode. Die Genauigkeit des Verfahrens wird dadurch verbessert, daß neben quadratischen Splines geeignete Singularitätenfunktionen als zusätzliche Test- und Ansatzfunktionen verwendet werden. Wir analysieren die Konsistenz der verwendeten numerischen Integrationen und erhalten asymptotische Fehlerabschätzungen der voll diskretisierten Näherungsgleichungen. Diese sind von den gleichen optimalen Ordnungen wie die entsprechenden Galerkin-Fehler.

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Authors and Affiliations

  1. Fachbereich Mathematik, Schlossgartenstrasse 7, D-6100, Darmstadt, Federal Republic of Germany

    U. Lamp, T. Schleicher & W. L. Wendland

  2. School of Mathematics, Georgia Inst. Technology, 30332, Atlanta, GA, U.S.A.

    E. Stephan

Authors
  1. U. Lamp
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  2. T. Schleicher
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  3. E. Stephan
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  4. W. L. Wendland
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Lamp, U., Schleicher, T., Stephan, E. et al. Galerkin collocation for an improved boundary element method for a plane mixed boundary value problem. Computing 33, 269–296 (1984). https://doi.org/10.1007/BF02242273

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  • DOI: https://doi.org/10.1007/BF02242273

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