Premium
A posteriori error analysis for nonconforming approximations of an anisotropic elliptic problem
Author(s) -
Achchab Boujemâa,
Agouzal Abdellatif,
Majdoubi Adil,
Meskine Driss,
Souissi Ali
Publication year - 2015
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21929
Subject(s) - mathematics , piecewise , estimator , a priori and a posteriori , robustness (evolution) , finite element method , helmholtz equation , partial differential equation , mathematical analysis , boundary value problem , statistics , philosophy , biochemistry , chemistry , physics , epistemology , gene , thermodynamics
We develop in this article an a posteriori error estimator for the P 1 ‐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