Convergence rates for adaptive finite elements

Details Convergence rates for adaptive finite elements Convergence rates for adaptive finite elements

2008-03-27

arxiv.org/abs/0803.3824v1

Mathematics

Numerical Analysis

Scientific paper

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.

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