Locally supported, piecewise polynomial biorthogona wavelets on non-uniform meshes

Abstract

In this paper, biorthogonal wavelets are constructed on non-uniform meshes. Both primal and dual wavelets are explicitly given locally supported, continuous piecewise polynomials. The wavelets generate Riesz bases for the Sobolev spaces H s for j s j < 3 2 . The wavelets at the primal side span standard Lagrange nite element spaces.