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arXiv · 0803.3824

Convergence rates for adaptive finite elements

Fernando D. Gaspoz·Pedro Morin
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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.

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Fernando D. Gaspoz, Pedro Morin. 2008-03-27. Convergence rates for adaptive finite elements. https://arxiv.org/abs/0803.3824

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