This paper is concerned with some theoretical foundations for adaptive numerical methods for elliptic boundary value problems. The approximation order that can be achieved by such an adaptive method is determined by certain Besov regularity of the weak solution. We study Besov regularity for second order elliptic problems in bounded domains in ℝd. The investigations are based on intermediate Schauder estimates and on some potential theoretic framework. Moreover, we use characterizations of Besov spaces by wavelet expansions.
elliptic boundary value problems adaptive methods nonlinear approximation Besov spaces wavelets Schauder estimates potential theory
AMS Subject Classifications
primary 35B65 secondary 31B10 41A46 46E35 65N30
This is a preview of subscription content, log in to check access.