Approximation classes for adaptive time-stepping finite element methods

03/10/2021

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by   Marcelo Actis, et al.

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We study approximation classes for adaptive time-stepping finite element methods for time-dependent Partial Differential Equations (PDE). We measure the approximation error in L_2([0,T)×Ω) and consider the approximation with discontinuous finite elements in time and continuous finite elements in space, of any degree. As a byproduct we define Besov spaces for vector-valued functions on an interval and derive some embeddings, as well as Jackson- and Whitney-type estimates.