Convergence rates for adaptive finite elements
Numerical Analysis
2008-03-28 v1
Abstract
In this article we prove that it is possible to construct, using newest-vertex bisection, meshes that equidistribute the error in -norm, whenever the function to approximate can be decomposed as a sum of a regular part plus a singular part with singularities around a finite number of points. This decomposition is usual in regularity results of Partial Differential Equations (PDE). As a consequence, the meshes turn out to be quasi-optimal, and convergence rates for adaptive finite element methods (AFEM) using Lagrange finite elements of any polynomial degree are obtained.
Cite
@article{arxiv.0803.3824,
title = {Convergence rates for adaptive finite elements},
author = {Fernando D. Gaspoz and Pedro Morin},
journal= {arXiv preprint arXiv:0803.3824},
year = {2008}
}