English

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.

Keywords

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

R2 v1 2026-06-21T14:43:12.084Z