Structure-preserving approximation of the non-isothermal Cahn-Hilliard system

2025/06/30 by Brunk, Aaron, Lukacova-Medvidova, Maria, Schumann, Dennis
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2506.23933

Abstract

We propose and analyze a structure-preserving approximation of the non-isothermal Cahn-Hilliard equation using conforming finite elements for the spatial discretization and a problem-specific mixed explicit-implicit approach for the temporal discretization. To ensure the preservation of structural properties, i.e. conservation of mass and internal energy as well as entropy production, we introduce a suitable variational formulation for the continuous problem, based on the entropy equation. Analytical findings are supported by numerical tests, including convergence analysis.

Citations

• Nonisothermal Cahn-Hilliard Navier-Stokes system
• Variational approximation for a non-isothermal coupled phase-field system: Structure-preservation & Nonlinear stability
• On a Cahn-Hilliard system with source term and thermal memory
• Temperature dependent extensions of the Cahn-Hilliard equation
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• On a non-isothermal Cahn-Hilliard model for tumor growth
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