High order, semi-implicit, energy stable schemes for gradient flows

被引：2

作者：

Zaitzeff, Alexander ^{[1
]}

Esedoglu, Selim ^{[1
]}

Garikipati, Krishna ^{[2
,3
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] Univ Michigan, Michigan Inst Computat Discovery & Engn, Dept Mech Engn, Ann Arbor, MI 48109 USA

[3] Univ Michigan, Michigan Inst Computat Discovery & Engn, Dept Math, Ann Arbor, MI 48109 USA

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2021年 / 447卷

关键词：

Gradient flows; IMEX; Runge-Kutta; Minimizing movements; High order schemes; Stability; CONVEX SPLITTING SCHEMES; FINITE-DIFFERENCE SCHEME; NONLOCAL CAHN-HILLIARD; RUNGE-KUTTA SCHEMES; NUMERICAL-METHODS; ALLEN-CAHN; 2ND-ORDER; TIME; CONVERGENCE; EQUATION;

D O I：

10.1016/j.jcp.2021.110688

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We introduce a class of high order accurate, semi-implicit Runge-Kutta schemes in the general setting of evolution equations that arise as gradient flow for a cost function, possibly with respect to an inner product that depends on the solution, and we establish their energy stability. This class includes as a special case high order, unconditionally stable schemes obtained via convexity splitting. The new schemes are demonstrated on a variety of gradient flows, including partial differential equations that are gradient flow with respect to the Wasserstein (mass transport) distance. (C) 2021 Elsevier Inc. All rights reserved.

引用

页数：21

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