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Volume 12, Issue 2
On an Essential Estimate in the Analysis of Domain Decomposition Methods

Jin-Sheng Gu & Xian-Cheng Hu

J. Comp. Math., 12 (1994), pp. 132-137.

Published online: 1994-12

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  • Abstract

A class of nonconforming finite elements is considered in this paper, which is continuous only at the nodes of the quasi-uniform mesh. We show that there exists an essential estimate which indicates the equivalence relation, independent of the mesh parameter, between the energies of the nonconforming discrete harmonic extensions in different subdomains. The essential estimate is of great importance in the analysis of the nonoverlapping domain decomposition methods applied to second order partial differential equations discretized by nonconforming finite elements.

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@Article{JCM-12-132, author = {Gu , Jin-Sheng and Hu , Xian-Cheng}, title = {On an Essential Estimate in the Analysis of Domain Decomposition Methods}, journal = {Journal of Computational Mathematics}, year = {1994}, volume = {12}, number = {2}, pages = {132--137}, abstract = {

A class of nonconforming finite elements is considered in this paper, which is continuous only at the nodes of the quasi-uniform mesh. We show that there exists an essential estimate which indicates the equivalence relation, independent of the mesh parameter, between the energies of the nonconforming discrete harmonic extensions in different subdomains. The essential estimate is of great importance in the analysis of the nonoverlapping domain decomposition methods applied to second order partial differential equations discretized by nonconforming finite elements.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9282.html} }
TY - JOUR T1 - On an Essential Estimate in the Analysis of Domain Decomposition Methods AU - Gu , Jin-Sheng AU - Hu , Xian-Cheng JO - Journal of Computational Mathematics VL - 2 SP - 132 EP - 137 PY - 1994 DA - 1994/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9282.html KW - AB -

A class of nonconforming finite elements is considered in this paper, which is continuous only at the nodes of the quasi-uniform mesh. We show that there exists an essential estimate which indicates the equivalence relation, independent of the mesh parameter, between the energies of the nonconforming discrete harmonic extensions in different subdomains. The essential estimate is of great importance in the analysis of the nonoverlapping domain decomposition methods applied to second order partial differential equations discretized by nonconforming finite elements.

Gu , Jin-Sheng and Hu , Xian-Cheng. (1994). On an Essential Estimate in the Analysis of Domain Decomposition Methods. Journal of Computational Mathematics. 12 (2). 132-137. doi:
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