Convergence and quasi-optimal complexity of a simple adaptive finite element method

Roland Becker; Shipeng Mao

ESAIM: Mathematical Modelling and Numerical Analysis (2009)

  • Volume: 43, Issue: 6, page 1203-1219
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Becker, Roland, and Mao, Shipeng. "Convergence and quasi-optimal complexity of a simple adaptive finite element method." ESAIM: Mathematical Modelling and Numerical Analysis 43.6 (2009): 1203-1219. <http://eudml.org/doc/250644>.

@article{Becker2009,
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. },
author = {Becker, Roland, Mao, Shipeng},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Adaptive finite elements; a posteriori error analysis; convergence of adaptive algorithms; complexity estimates.; adaptive finite elements; a posteriori error analysis; complexity estimates; local mesh refinements},
language = {eng},
month = {8},
number = {6},
pages = {1203-1219},
publisher = {EDP Sciences},
title = {Convergence and quasi-optimal complexity of a simple adaptive finite element method},
url = {http://eudml.org/doc/250644},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Becker, Roland
AU - Mao, Shipeng
TI - Convergence and quasi-optimal complexity of a simple adaptive finite element method
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2009/8//
PB - EDP Sciences
VL - 43
IS - 6
SP - 1203
EP - 1219
AB - 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.
LA - eng
KW - Adaptive finite elements; a posteriori error analysis; convergence of adaptive algorithms; complexity estimates.; adaptive finite elements; a posteriori error analysis; complexity estimates; local mesh refinements
UR - http://eudml.org/doc/250644
ER -

References

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