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arXiv · 2602.14921

Approximation classes for the anisotropic space-time finite element method. An almost characterization

Pedro Morin·Cornelia Schneider·Nick Schneider
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Abstract

We study the approximation of $L_p$-functions, $p\in (0,\infty]$, on cylindrical space-time domains $\Omega_T:=[0,T]\times \Omega$, $0<T<\infty$, $\Omega\subset \R^d$ Lipschitz, $d\in \mathbb{N}$, with respect to continuous anisotropic space-time finite elements on prismatic meshes. In particular, we propose a suitable refinement technique which creates (locally refined) prismatic meshes with sufficient smoothness and the desired anisotropy, and prove complexity estimates. Furthermore, we define a (quasi-)interpolation operator on this type of meshes and use it to characterize the corresponding approximation classes by showing direct and inverse estimates in terms of anisotropic Besov norms.

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Pedro Morin, Cornelia Schneider, Nick Schneider. 2026-02-16. Approximation classes for the anisotropic space-time finite element method. An almost characterization. https://arxiv.org/abs/2602.14921

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