A second-order structure-preserving discretization for the Cahn-Hilliard/Allen-Cahn system with cross-kinetic coupling

Autor:	Brunk, Aaron, Egger, Herbert, Habrich, Oliver
Rok vydání:	2023
Předmět:	Mathematics - Numerical Analysis 35K52 35K55 65M60 82C26
Druh dokumentu:	Working Paper
Popis:	We study the numerical solution of a Cahn-Hilliard/Allen-Cahn system with strong coupling through state and gradient dependent non-diagonal mobility matrices. A fully discrete approximation scheme in space and time is proposed which preserves the underlying gradient flow structure and leads to dissipation of the free-energy on the discrete level. Existence and uniqueness of the discrete solution is established and relative energy estimates are used to prove optimal convergence rates in space and time under minimal smoothness assumptions. Numerical tests are presented for illustration of the theoretical results and to demonstrate the viability of the proposed methods. Comment: 23 pages, 14 figures, 1 table. arXiv admin note: text overlap with arXiv:2209.03849
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2308.01638 Zobrazit plný text záznamu View this record from Arxiv