Afem for the Laplace-Beltrami operator on graphs: Design and conditional contraction property
We present an adaptive finite element method (AFEM) of any polynomial degree for the Laplace-Beltrami operator on C1 graphs Γ in R{double-struck}d (d ≥ 2). We first derive residual-type a posteriori error estimates that account for the interaction of both the energy error in H1(Γ) and the surface er...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2011 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/75180 |
| Acesso em linha: | http://hdl.handle.net/11336/75180 |
| Access Level: | acceso abierto |
| Palavra-chave: | A Posteriori Error Estimate Adaptive Finite Element Method Bisection Contraction Energy And Geometric Errors Graphs Laplace-Beltrami Operator https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | We present an adaptive finite element method (AFEM) of any polynomial degree for the Laplace-Beltrami operator on C1 graphs Γ in R{double-struck}d (d ≥ 2). We first derive residual-type a posteriori error estimates that account for the interaction of both the energy error in H1(Γ) and the surface error in W∞1 (Γ) due to approximation of Γ. We devise a marking strategy to reduce the total error estimator, namely a suitably scaled sum of the energy, geometric, and inconsistency error estimators. We prove a conditional contraction property for the sum of the energy error and the total estimator; the conditional statement encodes resolution of Γ in W∞1. We conclude with one numerical experiment that illustrates the theory. |
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