שמור ב:
| Main Authors: | , , |
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| פורמט: | Preprint |
| יצא לאור: |
2026
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| נושאים: | |
| גישה מקוונת: | https://arxiv.org/abs/2602.14921 |
| תגים: |
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| _version_ | 1866908836732862464 |
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| author | Morin, Pedro Schneider, Cornelia Schneider, Nick |
| author_facet | Morin, Pedro Schneider, Cornelia Schneider, Nick |
| contents | We study the approximation of $L_p$-functions, $p\in (0,\infty]$, on cylindrical space-time domains $Ω_T:=[0,T]\times Ω$, $0<T<\infty$, $Ω\subset \R^d$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14921 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Approximation classes for the anisotropic space-time finite element method. An almost characterization Morin, Pedro Schneider, Cornelia Schneider, Nick Numerical Analysis We study the approximation of $L_p$-functions, $p\in (0,\infty]$, on cylindrical space-time domains $Ω_T:=[0,T]\times Ω$, $0<T<\infty$, $Ω\subset \R^d$ 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. |
| title | Approximation classes for the anisotropic space-time finite element method. An almost characterization |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2602.14921 |