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
[Un modèle de domaine fictif unifié pour des conditions aux limites immergées générales]

Présenté par : 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.

Résumé
Abstract

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.

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.

Reçu le : 2005-02-27
Accepté le : 2005-09-27
Publié le : 2005-11-07

DOI : 10.1016/j.crma.2005.09.046

Affiliations des auteurs :

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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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/

Bibliographie
Cité par

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