Edge residuals dominate a posteriori error estimates for linear finite element methods on anisotropic triangular and tetrahedral meshes |
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| Authors: | G Kunert and R Verfürth |
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| Institution: | (1) Fakult?t für Mathematik, TU Chemnitz, 09107 Chemnitz, Germany; e-mail: gerd.kunert@mathematik.tu-chemnitz.de , DE;(2) Fakult?t für Mathematik, Ruhr-Universit?t Bochum, 44780 Bochum, Germany; e-mail: rv@num1.ruhr-uni-bochum.de , DE |
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| Abstract: | Summary. Both for the - and -norms, we prove that, up to higher order perturbation terms, edge residuals yield global upper and local lower bounds on
the error of linear finite element methods on anisotropic triangular or tetrahedral meshes. We also show that, with a correct
scaling, edge residuals yield a robust error estimator for a singularly perturbed reaction-diffusion equation.
Received April 19, 1999 / Published online April 20, 2000 |
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| Keywords: | Mathematics Subject Classification (1991): 65N30 65N15 |
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