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 approac
h.
LAGA Tech. Rep. n. 1999-17