A robust nonconforming \(H^2\)-element (Q2701547): Difference between revisions
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A robust nonconforming \(H^2\)-element (English) | |||
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Finite element methods for some elliptic fourth-order singular perturbation problems are considered. It is shown that if such problems are discretized by the nonconforming Morley method, in a regime close to second-order elliptic equations, then the error increases. A counterexample is presented to show that the Morley method diverges for the reduced second-order equation.NEWLINENEWLINENEWLINEAn alternative to the Morley method is proposed to use a nonconforming \(H^2\)-element which is \(H^1\)-conforming. It is shown that the new finite element method converges in the energy norm uniformly in the perturbation parameter. | |||
| Property / review text: Finite element methods for some elliptic fourth-order singular perturbation problems are considered. It is shown that if such problems are discretized by the nonconforming Morley method, in a regime close to second-order elliptic equations, then the error increases. A counterexample is presented to show that the Morley method diverges for the reduced second-order equation.NEWLINENEWLINENEWLINEAn alternative to the Morley method is proposed to use a nonconforming \(H^2\)-element which is \(H^1\)-conforming. It is shown that the new finite element method converges in the energy norm uniformly in the perturbation parameter. / rank | |||
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| Property / reviewed by: Zbigniew Dżygadło / rank | |||
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Revision as of 14:33, 10 April 2025
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A robust nonconforming \(H^2\)-element |
scientific article |
Statements
19 February 2001
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singular perturbation
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nonconforming finite elements
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uniform error estimates
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uniform convergence
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fourth-order elliptic equation
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finite element methods
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nonconforming Morley method
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counterexample
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A robust nonconforming \(H^2\)-element (English)
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Finite element methods for some elliptic fourth-order singular perturbation problems are considered. It is shown that if such problems are discretized by the nonconforming Morley method, in a regime close to second-order elliptic equations, then the error increases. A counterexample is presented to show that the Morley method diverges for the reduced second-order equation.NEWLINENEWLINENEWLINEAn alternative to the Morley method is proposed to use a nonconforming \(H^2\)-element which is \(H^1\)-conforming. It is shown that the new finite element method converges in the energy norm uniformly in the perturbation parameter.
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