A \(C^{0}\) finite element method for the biharmonic problem without extrinsic penalization (Q2875715)
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scientific article; zbMATH DE number 6328565
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A \(C^{0}\) finite element method for the biharmonic problem without extrinsic penalization |
scientific article; zbMATH DE number 6328565 |
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11 August 2014
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biharmonic equation
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convergence
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finite element method
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stability
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numerical experiment
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Kirchhoff plates
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0.9461419
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0.93332934
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0.9273971
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0.9253276
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0.92222327
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0.91462433
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0.91003764
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0.90122056
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A \(C^{0}\) finite element method for the biharmonic problem without extrinsic penalization (English)
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A symmetric \(C^{0} \) finite element method is constructed and analyzed. This approach introduces one-sided second order derivatives and Hessian matrices to formulate the scheme. It is shown that the method is stable and converges with optimal order in a variety of norms. A distinctive feaure of the method is that the results hold without extrinsic penalization of the gradient across inerelement boundaries. Numerical experiments are given that support the theoretical results, and the extension to Kirchhoff plates is also discussed.
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