no. 4
Numerical Analysis/Partial Differential Equations
A domain embedding method for mixed boundary value problems
[Une méthode de domaine fictif pour des problèmes aux limites mixtes]

Présenté par : Roland Glowinski

Zhang, Sheng1
1 Department of Mathematics, Wayne State University, Detroit, MI 48202, USA
Comptes Rendus. Mathématique, Tome 343 (2006) no. 4, pp. 287-290.

Nous proposons une méthode de domaine fictif dans la résolution de problèmes elliptiques avec conditions aux limites mixtes. Nous établissons une estimation précise du taux de convergence de la solution d'un problème approché. La théorie donne un traitement unifié dans les cas de conditions aux limites de Dirichlet, de Neumann et de Robin.

We propose a domain embedding (fictitious domain) method for elliptic equations subject to mixed boundary conditions, and prove the sharp convergence rate. The theory provides a unified treatment for Dirichlet, Neumann, and Robin boundary conditions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.06.025
Zhang, Sheng 1

1 Department of Mathematics, Wayne State University, Detroit, MI 48202, USA 
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Zhang, Sheng. A domain embedding method for mixed boundary value problems. Comptes Rendus. Mathématique, Tome 343 (2006) no. 4, pp. 287-290. doi : 10.1016/j.crma.2006.06.025. http://www.numdam.org/articles/10.1016/j.crma.2006.06.025/

[1] Gilbarg, D.; Trudinger, N.S. Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983

[2] Glowinski, R.; Kuznetsov, Y. On the solution of the Dirichlet problem for linear elliptic operators by a distributed Lagrange multiplier method, C. R. Acad. Sci. Paris, Ser. I, Volume 327 (1998), pp. 693-698

[3] Glowinski, R.; Pan, T.W. Error estimate for fictitious domain/penalty/finite element methods, Calcolo, Volume 29 (1991), pp. 125-141

[4] Glowinski, R.; Pan, T.W.; Wells, R.O. Jr.; Zhou, X. Wavelet and finite element solutions for the Neumann problem using fictitious domains, J. Comput. Phys., Volume 126 (1996), pp. 40-51

[5] Zhang, S. Equivalence estimates for a class of singular perturbation problems, C. R. Acad. Sci. Paris, Ser. I, Volume 342 (2006), pp. 285-288

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