The wavelet Mortar method in the adaptative framework

Silvia Bertoluzza; Anne-Sophie Piquemal

doi:10.1016/j.crma.2003.11.034

Numerical Analysis

The wavelet Mortar method in the adaptative framework

Presented by: Olivier Pironneau

Silvia Bertoluzza ¹; Anne-Sophie Piquemal ¹

¹ IMATI-CNR, Via Ferrata 1, 27100 Pavia, Italy

Comptes Rendus. Mathématique, Volume 338 (2004) no. 8, pp. 653-656.

Abstract
Résumé

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.

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.

Received: 2003-01-06
Accepted: 2003-11-12
Published online: 2004-03-25

DOI: 10.1016/j.crma.2003.11.034

Author's affiliations:

Silvia Bertoluzza ¹; Anne-Sophie Piquemal ¹

¹ IMATI-CNR, Via Ferrata 1, 27100 Pavia, Italy

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     title = {The wavelet {Mortar} method in the adaptative framework},
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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/

References
Cited by

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[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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