On the Rate of Convergence of the Bergman-Vekua Method for the Numerical Solution of Elliptic Boundary Value Problems

We consider the Bergman-Vekua method of particular solutions for the numerical solution of elliptic boundary value problems. The rate of convergence is shown to depend on the smoothness of the solution or, equivalently for domains with smooth boundary, on the smoothness of the boundary data. For dom...

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Bibliographic Details
Published inSIAM journal on numerical analysis Vol. 11; no. 3; pp. 654 - 680
Main Author Eisenstat, Stanley C.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.06.1974
Subjects
Analytic functions
Approximation
Boundary value problems
Coefficients
Convergent boundaries
Eigenvalues
Mathematical integrals
Partial differential equations
Polynomials
Sine function
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Summary:We consider the Bergman-Vekua method of particular solutions for the numerical solution of elliptic boundary value problems. The rate of convergence is shown to depend on the smoothness of the solution or, equivalently for domains with smooth boundary, on the smoothness of the boundary data. For domains with piecewise smooth boundary, the introduction of certain singular particular solutions is shown to lead to a similar dependency. A method for solving the membrane eigenvalue problem is proposed and shown to have the same rate of convergence.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0036-1429
1095-7170
DOI:10.1137/0711053