Anisotropic mesh refinement in polyhedral domains: error estimates with data in \(L^{2}(\varOmega)\) (Q2877717)
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scientific article; zbMATH DE number 6334072
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Anisotropic mesh refinement in polyhedral domains: error estimates with data in \(L^{2}(\varOmega)\) |
scientific article; zbMATH DE number 6334072 |
Statements
25 August 2014
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elliptic boundary value problem
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edge and vertex singularities
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finite element method
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anisotropic mesh grading
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optimal control problem
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discrete compactness property
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error estimates
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Poisson equation
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quasi-interpolantion operator
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numerical result
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Anisotropic mesh refinement in polyhedral domains: error estimates with data in \(L^{2}(\varOmega)\) (English)
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The paper is concerned with the finite element solution of the Poisson equation with homogeneous Dirichlet boundary condition in a three-dimensional domain. The discretization error is analyzed for the piecewise linear approximation in the \(H^1 \) and \(L^2 \)-norms by using a new quasi-interpolation operator. This new quasi-interpolantion operator is introduced in order to prove the estimates. The approximation properties and numerical results are presented.
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