Convergence and quasi-optimal complexity of a simple adaptive finite element method
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 6, p. 1203-1219

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.

DOI : https://doi.org/10.1051/m2an/2009036
Classification:  65N12,  65N15,  65N30,  65N50
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {43},
number = {6},
year = {2009},
pages = {1203-1219},
doi = {10.1051/m2an/2009036},
zbl = {pre05636852},
mrnumber = {2588438},
language = {en},
url = {http://www.numdam.org/item/M2AN_2009__43_6_1203_0}
}

Becker, Roland; Mao, Shipeng. Convergence and quasi-optimal complexity of a simple adaptive finite element method. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 6, pp. 1203-1219. doi : 10.1051/m2an/2009036. http://www.numdam.org/item/M2AN_2009__43_6_1203_0/

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