| Issue |
ESAIM: M2AN
Volume 43, Number 6, November-December 2009
|
|
|---|---|---|
| Page(s) | 1203 - 1219 | |
| DOI | https://doi.org/10.1051/m2an/2009036 | |
| Published online | 21 August 2009 | |
Convergence and quasi-optimal complexity of a simple adaptive finite element method
1
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
2
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
Received:
27
July
2008
Revised:
17
April
2009
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.
Mathematics Subject Classification: 65N12 / 65N15 / 65N30 / 65N50
Key words: Adaptive finite elements / a posteriori error analysis / convergence of adaptive algorithms / complexity estimates.
© EDP Sciences, SMAI, 2009
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.