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Convergence and quasi-optimal complexityof a simple adaptive finite element method

Published online by Cambridge University Press:  21 August 2009

Roland Becker  and
Shipeng Mao
Roland Becker
Affiliation:
Laboratoire de Mathématiques Appliquées and INRIA Bordeaux Sud-Ouest Concha, Université de Pau, 64013 Pau Cedex, France. roland.becker@univ-pau.fr; beckerroland@me.com
Shipeng Mao
Affiliation:
Institute of Computational Mathematics and INRIA Bordeaux Sud-Ouest Concha, Chinese Academy of Sciences (CAS), Beijing, 100190, P. R. China. maosp@lsec.cc.ac.cn
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Abstract

We prove convergence and quasi-optimal complexity of an adaptive finite element algorithm on triangular meshes with standard mesh refinement. Our algorithm is based on an adaptive marking strategy. In each iteration, a simple edge estimator is compared to an oscillation term and the marking of cells for refinement is done according to the dominant contribution only. In addition, we introduce an adaptive stopping criterion for iterative solution which compares an estimator for the iteration error with the estimator for the discretization error.

Keywords

Adaptive finite elementsa posteriori error analysisconvergence of adaptive algorithmscomplexity estimates.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 43 , Issue 6 , November 2009 , pp. 1203 - 1219
Copyright
© EDP Sciences, SMAI, 2009

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