Comptes Rendus
no. 8
Numerical Analysis
The wavelet Mortar method in the adaptative framework
[La méthode de Mortar en ondelettes dans le cas adaptatif]

Présenté par : Olivier Pironneau

Silvia Bertoluzza1 ; Anne-Sophie Piquemal1
1 IMATI-CNR, Via Ferrata 1, 27100 Pavia, Italy
Comptes Rendus. Mathématique, Volume 338 (2004) no. 8, pp. 653-656.

Nous définissons l'extension de la méthode de Mortar en ondelettes dans le cadre d'une discrétisation non-uniforme, et construisons un espace de multiplicateurs, satisfaisant des hypothèses d'approximation et de stabilité, associé à des espaces d'ondelettes reliés par une condition de cône.

This paper is concerned with the extension to the case of a nonuniform discretization of the definition of the Mortar wavelet method. Given a (biorthogonal) non-uniform wavelet space, satisfying a suitable cone (or tree) condition, we construct a multiplier space satisfying the requirements for stability and approximation.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2003.11.034
Silvia Bertoluzza 1 ; Anne-Sophie Piquemal 1

1 IMATI-CNR, Via Ferrata 1, 27100 Pavia, Italy 
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Silvia Bertoluzza; Anne-Sophie Piquemal. The wavelet Mortar method in the adaptative framework. Comptes Rendus. Mathématique, Volume 338 (2004) no. 8, pp. 653-656. doi : 10.1016/j.crma.2003.11.034. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.11.034/

[1] C. Bernardi; Y. Maday; A.T. Patera Domain decomposition by the Mortar element method (H.G. Kaper; M. Garbey, eds.), Asymptotics and Numerical Methods for Partial Differential Equations with Critical Parameters, NATO Adv. Sci. Inst. Ser. C, vol. 384, 1993

[2] C. Bernardi; Y. Maday; A.T. Patera A new nonconforming approach to domain decomposition: the Mortar element method, Nonlinear Differential Equations and their Applications, College de France Seminars, 1994

[3] S. Bertoluzza, V. Perrier, The Mortar method in the wavelet context, LAGA Tech. Rep. n. 1999-17, and I.A.N.-C.N.R. Report n. 1153, M2AN, 1999, in press

[4] S. Bertoluzza, V. Perrier, Coupling wavelets and finite elements by the Mortar method, I.A.N.-C.N.R. Report n. 1991, 2000

[5] S. Bertoluzza, A.S. Piquemal, The Mortar wavelet method in the adaptative case, I.A.N.-C.N.R. Report n. 1272, 2002

[6] A. Cohen Numerical analysis of wavelet methods (P.G. Ciarlet; J.-L. Lions, eds.), Handbook in Numerical Analysis, vol. VII, Elsevier, 1999

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