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Some remarks about the hierarchical a posteriori error estimate
Author(s) -
Achchab B.,
Achchab S.,
Agouzal A.
Publication year - 2004
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.20016
Subject(s) - mathematics , a priori and a posteriori , estimator , quadratic equation , simple (philosophy) , finite element method , robustness (evolution) , partial differential equation , calculus (dental) , mathematical optimization , mathematical analysis , statistics , geometry , medicine , philosophy , physics , biochemistry , chemistry , epistemology , dentistry , gene , thermodynamics
The saturation assumption is widely used in a posteriori error analysis of finite element methods. It asserts, in its simplest form, that the solution can be approximated asymptotically better with quadratic than with linear finite elements. In this article, we show that a simple modification of this “hypothesis” is valid, and the proof of many authors can be made rigorous with this simple modification. We prove also the robustness of the estimator for a singularly perturbed problem. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004