Structure-preserving approximation of the non-isothermal Cahn-Hilliard system based on the entropy equation
Numerical Analysis
2026-02-05 v2 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2506.23933,
title = {Structure-preserving approximation of the non-isothermal Cahn-Hilliard system based on the entropy equation},
author = {Aaron Brunk and Dennis Höhn and Mária Lukáčová-Medvidová},
journal= {arXiv preprint arXiv:2506.23933},
year = {2026}
}