Defect corrections for multigrid solutions of the Dirichlet problem in general domains

Author:
Winfried Auzinger

Journal:
Math. Comp. **48** (1987), 471-484

MSC:
Primary 65B05; Secondary 65N20

DOI:
https://doi.org/10.1090/S0025-5718-1987-0878685-7

MathSciNet review:
878685

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Abstract: Recently, the technique of defect correction for the refinement of discrete solutions to elliptic boundary value problems has gained new acceptance in connection with the multigrid approach. In the present paper we give an analysis of a specific application, namely to finite-difference analogues of the Dirichlet problem for Helmholtz's equation, emphasizing the case of nonrectangular domains. A quantitative convergence proof is presented for a class of convex polygonal domains.

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DOI:
https://doi.org/10.1090/S0025-5718-1987-0878685-7

Article copyright:
© Copyright 1987
American Mathematical Society