The Wavelet Element Method (WEM) combines biorthogonal wavelet systems with the philosophy of Spectral Element Methods in order to obtain a biorthogonal wavelet system on fairly general bounded domains in some β«ήβ¬ n . The domain of interest is split into subdomains which are mapped to a simple reference domain, here n-dimensional cubes. Thus, one has to construct appropriate biorthogonal wavelets on the reference domain such that mapping them to each subdomain and matching along the interfaces leads to a wavelet system on the domain. In this paper we use adapted biorthogonal wavelet systems on the interval in such a way that tensor products of these functions can be used for the construction of wavelet bases 1 This work was partially supported by the following funds: in Italy, MURST ex-40% Analisi Numerica and CNR ST/74 Progetto Strategico Modelli e Metodi per la Matematica e l'Ingegneria; in Germany, DAAD Vigoni-Project Multilevel-Zerlegungsverfahren fu Β¨r Partielle Differentialgleichungen and DFG-Graduiertenkolleg Analyse und Konstruktion in der Mathematik at the RWTH Aachen.
2 This author is in particular grateful to Wolfgang Dahmen. Moreover, he thanks Gero NieΓen for helpful remarks concerning the presentation.