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

Fuente: arXiv
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Main Authors: Brunk, Aaron, Habrich, Oliver, Oyedeji, Timileyin David, Yang, Yangyiwei, Xu, Bai-Xiang
Format: Preprint
Published: 2023
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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