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

ESAIM: Mathematical Modelling and Numerical Analysis (2009)

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

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topBecker, 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 -

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