Premium
Nonlinear and adaptive frame approximation schemes for elliptic PDEs: Theory and numerical experiments
Author(s) -
Dahlke Stephan,
Fornasier Massimo,
Primbs Miriam,
Raasch Thorsten,
Werner Manuel
Publication year - 2009
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20407
Subject(s) - mathematics , discretization , elliptic operator , partial differential equation , nonlinear system , partial derivative , frame (networking) , benchmark (surveying) , boundary value problem , operator (biology) , differential operator , elliptic partial differential equation , mathematical analysis , computer science , telecommunications , biochemistry , chemistry , physics , geodesy , repressor , quantum mechanics , transcription factor , gene , geography
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