Convergence rates for adaptive finite elements

Abstract

In this article we prove that it is possible to construct, using newest-vertex bisection, meshes that equidistribute the error in $H^1$-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.


Published: IMA Journal of Numerical Analysis 2008; doi: 10.1093/imanum/drn039

Link: http://imajna.oxfordjournals.org/cgi/reprint/drn039?ijkey=aULHrx3AxOoNGTm&keytype=ref