Volume 13, Issue 4
The Convergence of Multigrid Methods for Solving Finite Element Equations in the Presence of Singularities

Y. Q. Huang & Y. X. Li

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J. Comp. Math., 13 (1995), pp. 315-324

Published online: 1995-08

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  • 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 more 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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@Article{JCM-13-315, author = {}, title = {The Convergence of Multigrid Methods for Solving Finite Element Equations in the Presence of Singularities}, journal = {Journal of Computational Mathematics}, year = {1995}, volume = {13}, number = {4}, pages = {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 more 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. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9273.html} }
TY - JOUR T1 - The Convergence of Multigrid Methods for Solving Finite Element Equations in the Presence of Singularities JO - Journal of Computational Mathematics VL - 4 SP - 315 EP - 324 PY - 1995 DA - 1995/08 SN - 13 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/jcm/9273.html KW - AB - 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 more 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.
Y. Q. Huang & Y. X. Li. (1970). The Convergence of Multigrid Methods for Solving Finite Element Equations in the Presence of Singularities. Journal of Computational Mathematics. 13 (4). 315-324. doi:
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