Nonlinear and adaptive frame approximation schemes for elliptic PDEs: Theory and numerical experiments
Stephan Dahlke, Massimo Fornasier, Miriam Primbs, Thorsten Raasch, Manuel Werner · Numerical Methods for Partial Differential Equations · 2008
Abstract This article is concerned with adaptive numerical frame methods for elliptic operator equations. We show how specific noncanonical frame expansions on domains can be constructed. Moreover, we study the approximation order of best n‐term frame approximation, which serves as the benchmark for the performance of adaptive schemes. We also discuss numerical experiments for second order elliptic boundary value problems in polygonal domains where the discretization is based on recent constructions of boundary adapted wavelet bases on the interval. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009