Convergence and quasi-optimal complexity of a simple adaptive finite element method
Laboratoire de Mathématiques Appliquées and INRIA Bordeaux Sud-Ouest Concha,
Université de Pau, 64013 Pau Cedex, France. email@example.com; firstname.lastname@example.org
2 Institute of Computational Mathematics and INRIA Bordeaux Sud-Ouest Concha, Chinese Academy of Sciences (CAS), Beijing, 100190, P. R. China. email@example.com
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