On approximation classes for adaptive time-stepping finite element methods

Abstract

We study approximation classes for adaptive time-stepping finite element methods for time-dependent partial differential equations. We measure the approximation error in |$L_2([0,T)\times \varOmega )$| and consider the approximation with discontinuous finite elements in time and continuous finite elements in space, of any degree. As a by-product we define anisotropic Besov spaces for Banach-space-valued functions on an interval and derive some embeddings, as well as Jackson- and Whitney-type estimates.

approximation classes, Besov spaces, Whitney estimate, adaptive time-stepping finite element methods, greedy algorithm