Work

Variational Approximation for a Non-Isothermal Coupled Phase-Field System: Structure-Preservation & Nonlinear Stability

Year: 2024

Type: article

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 with respect to 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.

Source: Computational Methods in Applied Mathematics

DOI: 10.1515/cmam-2023-0274

Authors: Aaron Brunk, Oliver Habrich, Timileyin David Oyedeji, Yangyiwei Yang, Bai-Xiang Xu

Institutions: Johannes Gutenberg University Mainz, Johannes Kepler University of Linz, Technische Universität Darmstadt

Language: English

Topic: Solidification and crystal growth phenomena

Subfield: Materials Chemistry

Field: Materials Science

Domain: Physical Sciences

Open Access status: green

Funder: Deutsche Forschungsgemeinschaft

Awards: G1724403501, Variationsmethoden für die quantitative PhasenfeldModellierung und Simulation von pulverbasierten additiven Fertigungsverfahren, G2551665434, G546635654