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The mortar method in the wavelet context. (English) Zbl 0995.65131

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.

The paper is essentially theoretical and does not include any numerical experiments. It is nicely written.

MSC:
65N55Multigrid methods; domain decomposition (BVP of PDE)
35J25Second order elliptic equations, boundary value problems
65N15Error bounds (BVP of PDE)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65T60Wavelets (numerical methods)