Merging the Bramble-Pasciak-Steinbach and the Crouzeix-Thomée criterion for \(H^1\)-stability of the \(L^2\)-projection onto finite element spaces (Q2759090)
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scientific article; zbMATH DE number 1680745
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Merging the Bramble-Pasciak-Steinbach and the Crouzeix-Thomée criterion for \(H^1\)-stability of the \(L^2\)-projection onto finite element spaces |
scientific article; zbMATH DE number 1680745 |
Statements
10 December 2001
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finite element methods
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\(H^1\)-stability
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\(L^2\)-projection
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nonconforming finite element schemes
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Merging the Bramble-Pasciak-Steinbach and the Crouzeix-Thomée criterion for \(H^1\)-stability of the \(L^2\)-projection onto finite element spaces (English)
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The author presents a more flexible version of the Bramble-Pasciak-Steinbach criterion [see \textit{J. H. Bramble, J. E. Pasciak} and \textit{O. Steinbach}, ibid. 71, No. 237, 147-156 (2002; reviewed above)] for \(H^1\)-stability of the \(L^2\)-projection onto finite element spaces. This criterion is applicable to all kinds of finite element spaces including nonconforming finite element spaces. Some examples are given where the Bramble-Pasciak-Steinbach criterion or the Crouzeix-Thomée criterion [see \textit{M. Crouzeix} and \textit{V. Thomée}, ibid. Math. Comput. 48, 521-532 (1987; Zbl 0637.41034)] is not applicable but the new modified Bramble-Pasciak-Steinbach criterion guarantees \(H^1\)-stability.
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