A posteriori \(L_2\) error estimation on anisotropic tetrahedral finite element meshes (Q2725337)
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scientific article; zbMATH DE number 1619137
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A posteriori \(L_2\) error estimation on anisotropic tetrahedral finite element meshes |
scientific article; zbMATH DE number 1619137 |
Statements
13 September 2002
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anisotropic meshes
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a posteriori error estimates
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finite element method
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Poisson equation
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matching function
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anisotropic interpolation
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numerical examples
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A posteriori \(L_2\) error estimation on anisotropic tetrahedral finite element meshes (English)
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An a posteriori error estimator with respect to the \(L_2\)-norm is established that is appropriate for anisotropic triangular or tetrahedral elements. It is applied to the Poisson equation, i.e., to a differential equation with isotropic coefficients and the anisotropy enters via the geometry. Reliable and efficient estimators are obtained if the anisotropy of the mesh corresponds to the anisotropy of the solution. In order to control this, the author introduces a matching function. The analysis is based on results for anisotropic interpolation and on inverse estimates for appropriate bubble functions on anisotropic meshes. A numerical example in 3D is presented. Here the anisotropy arises from an edge singularity.
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