WHY LARGE TIME-STEPPING METHODS FOR THE CAHN-HILLIARD EQUATION IS STABLE

Li, Dong1,2

2022-07-01

10.1090/mcom/3768

MATHEMATICS OF COMPUTATION   影响因子和分区

0025-5718

1088-6842

We consider the Cahn-Hilliard equation with standard double-well potential. We employ a prototypical class of first order in time semi-implicit methods with implicit treatment of the linear dissipation term and explicit extrapolation of the nonlinear term. When the dissipation coefficient is held small, a conventional wisdom is to add a judiciously chosen stabilization term in order to afford relatively large time stepping and speed up the simulation. In practical numerical implementations it has been long observed that the resulting system exhibits remarkable stability properties in the regime where the stabilization parameter is O(1), the dissipation coefficient is vanishingly small and the size of the time step is moderately large. In this work we develop a new stability theory to address this perplexing phenomenon.

Cahn-Hilliard maximum principle stabilization

SCI

英语

第一 ; 通讯

Mathematics

Mathematics, Applied

WOS:000834689600001

AMER MATHEMATICAL SOC

MATHEMATICS

Web of Science

1.Southern Univ Sci & Technol, SUSTech Int Ctr Math, Shenzhen, Peoples R China
2.Southern Univ Sci & Technol, Dept Math, Shenzhen, Peoples R China

Li, Dong. WHY LARGE TIME-STEPPING METHODS FOR THE CAHN-HILLIARD EQUATION IS STABLE[J]. MATHEMATICS OF COMPUTATION,2022,91(338).

Li, Dong.(2022).WHY LARGE TIME-STEPPING METHODS FOR THE CAHN-HILLIARD EQUATION IS STABLE.MATHEMATICS OF COMPUTATION,91(338).

Li, Dong."WHY LARGE TIME-STEPPING METHODS FOR THE CAHN-HILLIARD EQUATION IS STABLE".MATHEMATICS OF COMPUTATION 91.338(2022).