no. 21-22
Numerical Analysis
Ghost penalty
[La pénalisation fantôme]

Présenté par : Philippe G. Ciarlet

Burman, Erik1
1 Department of Mathematics, University of Sussex, BN1 9RF Brighton, UK
Comptes Rendus. Mathématique, Tome 348 (2010) no. 21-22, pp. 1217-1220.

Dans cette Note nous étudions une méthode de pénalisation simple pour des méthodes de domaine fictif. La méthode permet de contrôler la sensibilité du nombre de conditionnement du système linéaire en fonction du positionement du domaine par rapport au maillage.

In this Note we discuss a simple penalty method that allows to increase the robustness of fictitious domain methods. In particular the condition number of the matrix can be upper bounded independently of how the domain boundary intersects the computational mesh, under rather weak assumptions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.10.006
Burman, Erik 1

1 Department of Mathematics, University of Sussex, BN1 9RF Brighton, UK 
@article{CRMATH_2010__348_21-22_1217_0,
     author = {Burman, Erik},
     title = {Ghost penalty},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1217--1220},
     publisher = {Elsevier},
     volume = {348},
     number = {21-22},
     year = {2010},
     doi = {10.1016/j.crma.2010.10.006},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2010.10.006/}
}
TY  - JOUR
AU  - Burman, Erik
TI  - Ghost penalty
JO  - Comptes Rendus. Mathématique
PY  - 2010
SP  - 1217
EP  - 1220
VL  - 348
IS  - 21-22
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2010.10.006/
DO  - 10.1016/j.crma.2010.10.006
LA  - en
ID  - CRMATH_2010__348_21-22_1217_0
ER  - 
%0 Journal Article
%A Burman, Erik
%T Ghost penalty
%J Comptes Rendus. Mathématique
%D 2010
%P 1217-1220
%V 348
%N 21-22
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2010.10.006/
%R 10.1016/j.crma.2010.10.006
%G en
%F CRMATH_2010__348_21-22_1217_0
Burman, Erik. Ghost penalty. Comptes Rendus. Mathématique, Tome 348 (2010) no. 21-22, pp. 1217-1220. doi : 10.1016/j.crma.2010.10.006. http://www.numdam.org/articles/10.1016/j.crma.2010.10.006/

[1] Becker, R.; Burman, E.; Hansbo, P. A Nitsche extended finite element method for incompressible elasticity with discontinuous modulus of elasticity, Comput. Methods Appl. Mech. Engrg., Volume 98 (2009) no. 41–44, pp. 3352-3360

[2] Codina, R.; Baiges, J. Approximate imposition of boundary conditions in immersed boundary methods, Internat. J. Numer. Methods Engrg., Volume 80 (2009) no. 11, pp. 1379-1405

[3] Dautray, R.; Lions, J.-L. Mathematical Analysis and Numerical Methods for Science and Technology, Functional and Variational Methods, vol. 2, Springer-Verlag, Berlin, 1988

[4] Ern, A.; Guermond, J.-L. Evaluation of the condition number in linear systems arising in finite element approximations, M2AN Math. Model. Numer. Anal., Volume 40 (2006) no. 1, pp. 29-48

[5] Girault, V.; Glowinski, R. Error analysis of a fictitious domain method applied to a Dirichlet problem, Japan J. Indust. Appl. Math., Volume 12 (1995) no. 3, pp. 487-514

[6] Hansbo, A.; Hansbo, P. An unfitted finite element method, based on Nitsche's method, for elliptic interface problems, Comput. Methods Appl. Mech. Engrg., Volume 191 (2002) no. 47–48, pp. 5537-5552

[7] Haslinger, J.; Renard, Y. A new fictitious domain approach inspired by the extended finite element method, SIAM J. Numer. Anal., Volume 47 (2009) no. 2, pp. 1474-1499

[8] Maury, B. Numerical analysis of a finite element/volume penalty method, SIAM J. Numer. Anal., Volume 47 (2009) no. 2, pp. 1126-1148

[9] Nitsche, J. Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind, Abh. Math. Sem. Univ. Hamburg, Volume 36 (1971), pp. 9-15

Cité par Sources :