Variational approximation for a non-isothermal coupled phase-field system: Structure-preservation & Nonlinear stability
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917737808265216 |
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| author | Brunk, Aaron Habrich, Oliver Oyedeji, Timileyin David Yang, Yangyiwei Xu, Bai-Xiang |
| author_facet | Brunk, Aaron Habrich, Oliver Oyedeji, Timileyin David Yang, Yangyiwei Xu, Bai-Xiang |
| contents | A Cahn-Hilliard-Allen-Cahn phase-field model coupled with a heat transfer equation, particularly with full non-diagonal mobility matrices, is studied. After reformulating the problem w.r.t. the inverse of temperature, we proposed and analysed a structure-preserving approximation for the semi-discretisation in space and then a fully discrete approximation using conforming finite elements and time-stepping methods. We prove structure-preserving property and discrete stability using relative entropy methods for the semi-discrete and fully discrete case. The theoretical results are illustrated by numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14566 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Variational approximation for a non-isothermal coupled phase-field system: Structure-preservation & Nonlinear stability Brunk, Aaron Habrich, Oliver Oyedeji, Timileyin David Yang, Yangyiwei Xu, Bai-Xiang Numerical Analysis Analysis of PDEs A Cahn-Hilliard-Allen-Cahn phase-field model coupled with a heat transfer equation, particularly with full non-diagonal mobility matrices, is studied. After reformulating the problem w.r.t. the inverse of temperature, we proposed and analysed a structure-preserving approximation for the semi-discretisation in space and then a fully discrete approximation using conforming finite elements and time-stepping methods. We prove structure-preserving property and discrete stability using relative entropy methods for the semi-discrete and fully discrete case. The theoretical results are illustrated by numerical experiments. |
| title | Variational approximation for a non-isothermal coupled phase-field system: Structure-preservation & Nonlinear stability |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2312.14566 |