A posteriori error analysis for nonconforming approximations of an anisotropic elliptic problem |
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| Authors: | Boujemâa Achchab Abdellatif Agouzal Adil Majdoubi Driss Meskine Ali Souissi |
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| Affiliation: | 1. Department of Mathematics, Univ. Hassan 1, LM2CE‐LAMSAD, FSJES et EST Berrechid, Maroc;2. Department of Mathematics, U.M.R. 5208 ‐ Institut Camille Jordan, Université de Lyon 1. Bat. 1001, Villeurbanne, Cedex, France;3. Numerical Analysis Group, Applied Mathematical Laboratory, Department of Mathematics, Faculty of Sciences, Mohammed V University‐Agdal, Rabat, Morocco;4. Department of Mathematics, EST, Université Cadi Ayyad, Essaouira, Maroc |
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| Abstract: | We develop in this article an a posteriori error estimator for the P1‐nonconforming finite element approximation, for a diffusion‐reaction equation. We adopt the error in a constitutive law approach in two and three dimensional space, for not necessary piecewise constant data of problems. The efficiency and the reliability of our estimators are proved, neither Helmholtz decomposition of the error nor saturation assumption. The constants are explicitly given, which prove the robustness of these estimators. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 950–976, 2015 |
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| Keywords: | nonconforming finite elements a posteriori error estimator reconstruction technics |
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