A unified fictitious domain model for general embedded boundary conditions

Philippe Angot

doi:10.1016/j.crma.2005.09.046

Numerical Analysis/Mathematical Problems in Mechanics

A unified fictitious domain model for general embedded boundary conditions

Presented by: Philippe G. Ciarlet

Philippe Angot ¹

¹ LATP-CMI, UMR CNRS 6632, Université de la méditerranée, 39, rue F. Joliot-Curie, 13453 Marseille cedex 13, France

Comptes Rendus. Mathématique, Volume 341 (2005) no. 11, pp. 683-688.

Abstract
Résumé

This Note addresses the analysis of a new fictitious domain method for elliptic problems in order to handle general embedded boundary conditions (E.B.C.): Fourier, Neumann and Dirichlet conditions on an immersed interface. Our method is based on a recent model of fracture combining flux and solution jumps on the interface Σ separating the original domain $\tilde{Ω}$ from the auxiliary exterior domain $Ω_{e}$ . A class of methods is derived within the same unified formulation with either no penalty or exterior control in $Ω_{e}$ , or surface penalty on Σ, volume $H^{1}$ or $L^{2}$ penalty in $Ω_{e}$ , or both. The consistency (no penalty) or optimal error estimates with respect to the penalty parameter are proved for such methods.

Cette Note analyse une nouvelle méthode de domaine fictif pour des problèmes elliptiques afin d'imposer des conditions aux limites générales : Fourier, Neumann et Dirichlet sur une frontière immergée. Notre méthode est basée sur un récent modèle de fracture combinant les sauts de la solution et du flux sur une interface Σ séparant le domaine originel $\tilde{Ω}$ du domaine extérieur auxiliaire $Ω_{e}$ . Une classe de méthodes est proposée dans la même formulation unifiée avec soit, aucun contrôle extérieur ou pénalisation dans $Ω_{e}$ , soit une pénalisation de surface sur Σ, ou une pénalisation volumique $L^{2}$ ou $H^{1}$ dans $Ω_{e}$ ou les deux. La consistance (sans pénalisation) ou des estimations d'erreur optimales en fonction du paramètre de pénalisation sont démontrées pour de telles méthodes.

Received: 2005-02-27
Accepted: 2005-09-27
Published online: 2005-11-07

DOI: 10.1016/j.crma.2005.09.046

Author's affiliations:

Philippe Angot ¹

¹ LATP-CMI, UMR CNRS 6632, Université de la méditerranée, 39, rue F. Joliot-Curie, 13453 Marseille cedex 13, France

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     title = {A unified fictitious domain model for general embedded boundary conditions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {683--688},
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     volume = {341},
     number = {11},
     year = {2005},
     doi = {10.1016/j.crma.2005.09.046},
     language = {en},
}

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Philippe Angot. A unified fictitious domain model for general embedded boundary conditions. Comptes Rendus. Mathématique, Volume 341 (2005) no. 11, pp. 683-688. doi : 10.1016/j.crma.2005.09.046. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.09.046/

References
Cited by

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