Multilevel Pseudo-Wavelet Schemes: a Consistency Analysis

The study of this paper is devoted to the analysis of multilevel approximation schemes, in the context of multiresolution analysis. We have particular interest in expansions where the coefficients are obtained in terms of discrete convolutions of function point values with some specific wheights. In the first part we analyze aspects, such as, algorithm of construction, their accuracy and multilevel implementation for three cases: interpolation, quasi-interpolation and discrete projection. The second part is dedicated to hybrid formulations for the discretization of nonlinear differential operators. The idea is to combine two different approximation schemes: one approximation scheme is used for functions or linear terms; another one, defined in terms of function point values, is used for nonlinear operations. Taking the bilinear advection operator as a model, we establish the consistency of the discretizations in terms of the order of the truncation error.