The Mortar Method in the Wavelet Context
S. Bertoluzza and V. Perrier
This paper deals with the use of
wavelets in the framework of the Mortar method. We first review in an abstract
framework the theory of the Mortar Method for non conforming domain decomposition,
and point out some basic assumptions under which stability and convergence
of such method can be proven. We study the application of the Mortar Method
in the biorthogonal wavelet framework. In particular we define suitable
multiplier spaces for imposing weak continuity. Unlike in the classical
mortar method, such multiplier spaces are not a subset of the space of
traces of interior functions, but rather of their duals. For the resulting
method, we provide with an error estimate, which is optimal in the geometrically
conforming case. We also study an almost diagonal preconditioner based
on using wavelet preconditioners as building blocks in a substructuring
approach.
LAGA Tech. Rep. n. 1999-17
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