Volume 16, Issue 5
Multigrid Methods for Morley Element on Nonnested Meshes

Zhong-ci Shi & Zheng-hui Xie

DOI:

J. Comp. Math., 16 (1998), pp. 385-394

Published online: 1998-10

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  • Abstract

In this paper, we consider some multigrid algorithms for the biharmonic problem discretized by Morley element on nonnested meshes. Through taking the averages of the nodal variables we construct an intergrid transfer operator that satisfies a certain stable approximation property. The so-called regularity-approximation assumption is then established. Optimal convergence properties of the $W$-cycle and a uniform condition number estimate for the variable $V$-cycle preconditioner are presented. This technique is applicable to other nonconforming plate elements.

  • Keywords

Multigrid method Morley element Nonnested meshes

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@Article{JCM-16-385, author = {}, title = {Multigrid Methods for Morley Element on Nonnested Meshes}, journal = {Journal of Computational Mathematics}, year = {1998}, volume = {16}, number = {5}, pages = {385--394}, abstract = { In this paper, we consider some multigrid algorithms for the biharmonic problem discretized by Morley element on nonnested meshes. Through taking the averages of the nodal variables we construct an intergrid transfer operator that satisfies a certain stable approximation property. The so-called regularity-approximation assumption is then established. Optimal convergence properties of the $W$-cycle and a uniform condition number estimate for the variable $V$-cycle preconditioner are presented. This technique is applicable to other nonconforming plate elements. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9169.html} }
TY - JOUR T1 - Multigrid Methods for Morley Element on Nonnested Meshes JO - Journal of Computational Mathematics VL - 5 SP - 385 EP - 394 PY - 1998 DA - 1998/10 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9169.html KW - Multigrid method KW - Morley element KW - Nonnested meshes AB - In this paper, we consider some multigrid algorithms for the biharmonic problem discretized by Morley element on nonnested meshes. Through taking the averages of the nodal variables we construct an intergrid transfer operator that satisfies a certain stable approximation property. The so-called regularity-approximation assumption is then established. Optimal convergence properties of the $W$-cycle and a uniform condition number estimate for the variable $V$-cycle preconditioner are presented. This technique is applicable to other nonconforming plate elements.
Zhong-ci Shi & Zheng-hui Xie. (1970). Multigrid Methods for Morley Element on Nonnested Meshes. Journal of Computational Mathematics. 16 (5). 385-394. doi:
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