Convergence rates for adaptive finite elements

In this article, we prove that it is possible to construct, using newest vertex bisection, meshes that equidistribute the error in the H1-norm whenever the function to be approximated can be decomposed as a sum of a regular part plus a singular part with singularities around a finite number of point...

ver descrição completa

Detalhes bibliográficos
Autores: Gaspoz, Fernando Daniel, Morin, Pedro
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2008
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/186275
Acesso em linha:http://hdl.handle.net/11336/186275
Access Level:acceso abierto
Palavra-chave:ADAPTIVE FINITE ELEMENTS
CONVERGENCE RATES
OPTIMALITY
REGULARITY
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descrição
Resumo:In this article, we prove that it is possible to construct, using newest vertex bisection, meshes that equidistribute the error in the H1-norm whenever the function to be approximated 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. As a consequence, the meshes turn out to be quasi-optimal, and convergence rates for adaptive finite-element methods using Lagrange finite elements of any polynomial degree are obtained.