Relative energy estimates for the Cahn-Hilliard equation with concentration dependent mobility

Autor:	Brunk, Aaron, Egger, Herbert, Habrich, Oliver, Lukacova-Medvidova, Maria
Rok vydání:	2021
Předmět:	Mathematics - Numerical Analysis Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	Based on relative energy estimates, we study the stability of solutions to the Cahn-Hilliard equation with concentration dependent mobility with respect to perturbations. As a by-product of our analysis, we obtain a weak-strong uniqueness principle on the continuous level under realistic regularity assumptions on strong solutions. We then show that the stability estimates can be further inherited almost verbatim by appropriate Galerkin approximations in space and time. This allows us to derive sharp bounds for the discretization error in terms of certain projection errors and to establish order-optimal a-priori error estimates for semi- and fully discrete approximation schemes. Comment: 27 pages, 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2102.05704 Zobrazit plný text záznamu View this record from Arxiv