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arXiv · 2312.14566

Variational approximation for a non-isothermal coupled phase-field system: Structure-preservation & Nonlinear stability

Aaron Brunk·Oliver Habrich·Timileyin David Oyedeji·Yangyiwei Yang·Bai-Xiang Xu
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Abstract

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.

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Aaron Brunk, Oliver Habrich, Timileyin David Oyedeji, Yangyiwei Yang, Bai-Xiang Xu. 2024-07-31. Variational approximation for a non-isothermal coupled phase-field system: Structure-preservation & Nonlinear stability. https://arxiv.org/abs/2312.14566

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