Geometry Error Analysis of a parametric mapping for Higher Order Unfitted Space-Time Methods
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910871990566912 |
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| author | Heimann, Fabian Lehrenfeld, Christoph |
| author_facet | Heimann, Fabian Lehrenfeld, Christoph |
| contents | In [Heimann, Lehrenfeld, Preuß, SIAM J. Sci. Comp. 45(2), 2023, B139 - B165] new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher-order accuracy in space and time have been introduced. For geometrically higher-order accuracy a parametric mapping on a background space-time tensor-product mesh has been used. In this paper, we concentrate on the geometrical accuracy of the approximation and derive rigorous bounds for the distance between the realized and an ideal mapping in different norms and derive results for the space-time regularity of the parametric mapping. These results are important and lay the ground for the error analysis of corresponding unfitted space-time finite element methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_02348 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Geometry Error Analysis of a parametric mapping for Higher Order Unfitted Space-Time Methods Heimann, Fabian Lehrenfeld, Christoph Numerical Analysis In [Heimann, Lehrenfeld, Preuß, SIAM J. Sci. Comp. 45(2), 2023, B139 - B165] new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher-order accuracy in space and time have been introduced. For geometrically higher-order accuracy a parametric mapping on a background space-time tensor-product mesh has been used. In this paper, we concentrate on the geometrical accuracy of the approximation and derive rigorous bounds for the distance between the realized and an ideal mapping in different norms and derive results for the space-time regularity of the parametric mapping. These results are important and lay the ground for the error analysis of corresponding unfitted space-time finite element methods. |
| title | Geometry Error Analysis of a parametric mapping for Higher Order Unfitted Space-Time Methods |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2311.02348 |