Unconditionally Energy Stable DG Schemes for the Swift-Hohenberg Equation

被引:22
|
作者
Liu, Hailiang [1 ]
Yin, Peimeng [1 ]
机构
[1] Iowa State Univ, Dept Math, Ames, IA 50011 USA
基金
美国国家科学基金会;
关键词
Swift-Hohenberg equation; Energy stability; DG method; Implicit-explicit time stepping; CAHN-HILLIARD;
D O I
10.1007/s10915-019-01038-6
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The Swift-Hohenberg equation as a central nonlinear model in modern physics has a gradient flow structure. Here we introduce fully discrete discontinuous Galerkin (DG) schemes for a class of fourth order gradient flow problems, including the nonlinear Swift-Hohenberg equation, to produce free-energy-decaying discrete solutions, irrespective of the time step and the mesh size. We exploit and extend the mixed DG method introduced in Liu and Yin (J Sci Comput 77:467-501, 2018) for the spatial discretization, and the "Invariant Energy Quadratization" method for the time discretization. The resulting IEQ-DG algorithms are linear, thus they can be efficiently solved without resorting to any iteration method. We actually prove that these schemes are unconditionally energy stable. We present several numerical examples that support our theoretical results and illustrate the efficiency, accuracy and energy stability of our new algorithm. The numerical results on two dimensional pattern formation problems indicate that the method is able to deliver comparable patterns of high accuracy.
引用
收藏
页码:789 / 819
页数:31
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