Semi-coarsening AMLI algorithms for elasticity problems (Q2716338)
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scientific article; zbMATH DE number 1602683
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Semi-coarsening AMLI algorithms for elasticity problems |
scientific article; zbMATH DE number 1602683 |
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10 June 2001
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almost incompressible elasticity
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algebraic multilevel method
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finite elements
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convergence
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mesh refinement
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Semi-coarsening AMLI algorithms for elasticity problems (English)
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0.88617146
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0.8784592
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0.87617046
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0.8703095
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0.8686035
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0.8665259
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0.8646433
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0.8626717
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The author starts with analysis of approximation of a two-dimensional elasticity problem by bilinear rectangle finite elements with two semi-coarsening refinement procedures. For each semi-coarsening, the author gives new estimates for the constant \(\gamma \) in the strengthened Cauchy-Bunyakowski-Schwarz inequality that is independent of the Poisson ratio. The constant is then used in the convergence analysis of the algebraic multilevel iteration (AMLI) method proposed by \textit{O. Axelsson} and \textit{P. S. Vassilevski} [Numer. Math. 56, 157-177 (1989; Zbl 0673.65069)]. In particular, for balanced semi-coarsening mesh refinement, the author gets the optimal rate of convergence independent on the Poisson ratio. The latter result grants fast convergence even for almost incompressible elasticity problems.
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