We study approximation classes for adaptive time-stepping finite element methods for time-dependent partial differential equations. We measure the approximation error in L₂([0,T)× ) 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.
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Actis et al. (2022) studied this question.
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