A posteriori L2 error estimation on anisotropic tetrahedral finite element meshes |
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Authors: | Kunert Gerd |
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Institution: |
1 TU Chemnitz, Fakultät für Mathematik, D-09107 Chemnitz, Germany, e-mail: gkunert{at}mathematik.tu-chemnitz.de
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Abstract: | A new a posteriori L2 norm error estimator is proposed for thePoisson equation. The error estimator can be applied to anisotropictetrahedral or triangular finite element meshes. The estimatoris rigorously analysed for Dirichlet and Neumann boundary conditions. The lower error bound relies on specifically designed anisotropicbubble functions and the corresponding inverse inequalities.The upper error bound utilizes non-standard anisotropic interpolationestimates. Its proof requires H2 regularity of the Poisson problem,and its quality depends on how good the anisotropic mesh resolvesthe anisotropy of the problem. This is measured by a so-calledmatching function. A numerical example supports the anisotropic error analysis. |
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Keywords: | L2 error estimation anisotropic solution anisotropic mesh tetrahedral element |
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