After reviewing some of the properties of wavelet bases, and in particular the property of characterisation of function spaces via wavelet coefficients, we describe two new approaches to, respectively, stabilisation of numerically unstable PDE's and to non linear (adaptive) solution of PDE's, which are made possible by these properties.

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,...

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,...

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