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...
| Autores: | , |
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| 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 |
| 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. |
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