Approximation classes for adaptive time-stepping finite element methods

2021/03/10 by Marcelo Actis, Actis, Marcelo, Pedro Morín +3 · 1 citation
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Numerical methods for differential equations #Electromagnetic Simulation and Numerical Methods

paper · pdf · doi:10.48550/arxiv.2103.06088

Abstract

We study approximation classes for adaptive time-stepping finite element methods for time-dependent Partial Differential Equations (PDE). We measure the approximation error in L₂([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.

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