Robust a posteriori error control for the Allen-Cahn equation with variable mobility
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911797570699264 |
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| author | Brunk, Aaron Giesselmann, Jan Lukacova-Medvidova, Maria |
| author_facet | Brunk, Aaron Giesselmann, Jan Lukacova-Medvidova, Maria |
| contents | In this work, we derive a $γ$-robust a posteriori error estimator for finite element approximations of the Allen-Cahn equation with variable non-degenerate mobility. The estimator utilizes spectral estimates for the linearized steady part of the differential operator as well as a conditional stability estimate based on a weighted sum of Bregman distances, based on the energy and a functional related to the mobility. A suitable reconstruction of the numerical solution in the stability estimate leads to a fully computable estimator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08898 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Robust a posteriori error control for the Allen-Cahn equation with variable mobility Brunk, Aaron Giesselmann, Jan Lukacova-Medvidova, Maria Numerical Analysis Analysis of PDEs In this work, we derive a $γ$-robust a posteriori error estimator for finite element approximations of the Allen-Cahn equation with variable non-degenerate mobility. The estimator utilizes spectral estimates for the linearized steady part of the differential operator as well as a conditional stability estimate based on a weighted sum of Bregman distances, based on the energy and a functional related to the mobility. A suitable reconstruction of the numerical solution in the stability estimate leads to a fully computable estimator. |
| title | Robust a posteriori error control for the Allen-Cahn equation with variable mobility |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2403.08898 |