Anisotropic nonconforming Crouzeix-Raviart type FEM for second-order elliptic problems (Q764630)
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scientific article; zbMATH DE number 6014579
| Language | Label | Description | Also known as |
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| English | Anisotropic nonconforming Crouzeix-Raviart type FEM for second-order elliptic problems |
scientific article; zbMATH DE number 6014579 |
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Anisotropic nonconforming Crouzeix-Raviart type FEM for second-order elliptic problems (English)
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13 March 2012
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The authors consider the 2D Poisson equation along with homogeneous Dirichlet data and the (triangular) Crouzeix-Raviart element on anisotropic grids (satisfying a maximal angle and a coordinate condition) for its numerical solution. Referring instead of [\textit{T. Apel}, Anisotropic finite elements: Local estimates and applications. Advances in Numerical Mathematics. Leipzig: Teubner. Chemnitz: Technische Univ. (1999; Zbl 0934.65121)], to an interpolation error estimate for anisotropic grids of \textit{D. Shi} and \textit{H. Guan}, [Hokkaido Math. J. 36, No. 4, 687--709 (2007; Zbl 1181.65100)], they prove optimal error estimates for their problem in the element-wise \(H^1\)- and the \(L_2\)-norm. Numerical results verify the theoretical findings.
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second order elliptic problem
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Crouzeix-Raviart element
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anisotropic grids
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optimal error estimates
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finite element method (FEM)
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Poisson equation
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numerical results
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0.91579497
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0.9129178
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0.9032467
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