The mortar method in the wavelet context

This paper deals with the use of wavelets in the framework of the Mortar me thod. We first review in an abstract framework the theory of the mortar met hod for non conforming domain decomposition, and point out some basic assum ptions under which stability and convergence of such method can be proven. We study the application of the mortar method in the biorthogonal wavelet f ramework. In particular we define suitable multiplier spaces for imposing w eak continuity. Unlike in the classical mortar method, such multiplier spac es are not a subset of the space of traces of interior functions, but rathe r of their duals. For the resulting method, we provide with an error estimate, which is optim al in the geometrically conforming case.