Convergence and Optimal Complexity of Adaptive Finite Element Methods
Numerical Analysis
2010-02-05 v1
Abstract
In this paper, we study adaptive finite element approximations in a perturbation framework, which makes use of the existing adaptive finite element analysis of a linear symmetric elliptic problem. We prove the convergence and complexity of adaptive finite element methods for a class of elliptic partial differential equations. For illustration, we apply the general approach to obtain the convergence and complexity of adaptive finite element methods for a nonsymmetric problem, a nonlinear problem as well as an unbounded coefficient eigenvalue problem.
Cite
@article{arxiv.1002.0887,
title = {Convergence and Optimal Complexity of Adaptive Finite Element Methods},
author = {Lianhua He and Aihui Zhou},
journal= {arXiv preprint arXiv:1002.0887},
year = {2010}
}
Comments
30pages, 14figures