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Zbl 0995.65131
Bertoluzza, Silvia; Perrier, Valérie
The mortar method in the wavelet context. (English)
[J] M2AN, Math. Model. Numer. Anal. 35, No.4, 647-673 (2001). ISSN 0764-583X; ISSN 1290-3841/e

This paper analyzes mathematically the use of wavelets in the framework of the mortar method. It starts with the reviews of the theory of the mortar method for non-conforming domain decomposition; in particular, it points out some basic assumptions under which stability and convergence of such method can be proved. Next, it analyzes the construction of mortar approximation spaces in the biorthogonal wavelet framework. An a priori error estimate is given and it is optimal in the geometrically conforming case.\par The paper is essentially theoretical and does not include any numerical experiments. It is nicely written.
[Michel Bernadou (Paris La Defense)]

MSC 2000:: *65N55 Multigrid methods; domain decomposition (BVP of PDE)
35J25 Second order elliptic equations, boundary value problems
65N15 Error bounds (BVP of PDE)
65N30 Finite numerical methods (BVP of PDE)
65T60 Wavelets

Keywords: domain decomposition; mortar method; wavelet approximation; stability; convergence; error estimate

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