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Abstract: In this article we prove that it is possible to construct, usingnewest-vertex bisection, meshes that equidistribute the error in $H^1$-norm,whenever the function to approximate can be decomposed as a sum of a regularpart plus a singular part with singularities around a finite number of points.This decomposition is usual in regularity results of Partial DifferentialEquations PDE. As a consequence, the meshes turn out to be quasi-optimal, andconvergence rates for adaptive finite element methods AFEM using Lagrangefinite elements of any polynomial degree are obtained.



Autor: Fernando D. Gaspoz, Pedro Morin

Fuente: https://arxiv.org/



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