Exponential convergence of adaptive quarklet approximation

Abstract

This paper is concerned with approximation properties of polynomially enriched wavelet systems, so-called quarklet frames. We show that certain model singularities that arise in elliptic boundary value problems on polygonal domains can be approximated from the span of such quarklet systems at inverse-exponential rates. In order to realize these, we combine spatial refinement in the vicinity of the singularities with suitable growth of the polynomial degrees in regions where the solution is smooth, similar to adaptive hp-finite element approximation.