The Convergence of Multigrid Methods for Solving Finite Element Equations in the Presence of Singularities
Year: 1995
Journal of Computational Mathematics, Vol. 13 (1995), Iss. 4 : pp. 315–324
Abstract
We analyze the convergence of multigrid methods applied to finite element equations of second order with singularities caused by reentrant angles and abrupt changes in the boundary conditions. Provided much weaker demand of classical multigrid proofs, it is shown in this paper that, for symmetric and positive definite problems in the presence of singularities, multigrid algorithms with even one smoothing step converge at a rate which is independent of the number of levels or unknowns. Furthermore, we extend this result to the nonsymmetric and indefinite problems.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1995-JCM-9273
Journal of Computational Mathematics, Vol. 13 (1995), Iss. 4 : pp. 315–324
Published online: 1995-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10