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.
Mots clés : adaptive finite elements, a posteriori error analysis, convergence of adaptive algorithms, complexity estimates
@article{M2AN_2009__43_6_1203_0, author = {Becker, Roland and Mao, Shipeng}, title = {Convergence and quasi-optimal complexity of a simple adaptive finite element method}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {1203--1219}, publisher = {EDP-Sciences}, volume = {43}, number = {6}, year = {2009}, doi = {10.1051/m2an/2009036}, mrnumber = {2588438}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2009036/} }
TY - JOUR AU - Becker, Roland AU - Mao, Shipeng TI - Convergence and quasi-optimal complexity of a simple adaptive finite element method JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2009 SP - 1203 EP - 1219 VL - 43 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2009036/ DO - 10.1051/m2an/2009036 LA - en ID - M2AN_2009__43_6_1203_0 ER -
%0 Journal Article %A Becker, Roland %A Mao, Shipeng %T Convergence and quasi-optimal complexity of a simple adaptive finite element method %J ESAIM: Modélisation mathématique et analyse numérique %D 2009 %P 1203-1219 %V 43 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2009036/ %R 10.1051/m2an/2009036 %G en %F M2AN_2009__43_6_1203_0
Becker, Roland; Mao, Shipeng. Convergence and quasi-optimal complexity of a simple adaptive finite element method. ESAIM: Modélisation mathématique et analyse numérique, Tome 43 (2009) no. 6, pp. 1203-1219. doi : 10.1051/m2an/2009036. http://www.numdam.org/articles/10.1051/m2an/2009036/
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