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

Autor:	Brunk, Aaron, Habrich, Oliver, Oyedeji, Timileyin David, Yang, Yangyiwei, Xu, Bai-Xiang
Rok vydání:	2023
Předmět:	Mathematics - Numerical Analysis Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	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. Comment: 20 pages; 3 figures; 6 pages appendix
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2312.14566 Zobrazit plný text záznamu View this record from Arxiv