On energy stable, maximum-principle preserving, second order BDF scheme with variable steps for the Allen-Cahn equation

03/01/2020
by   Hong-lin Liao, et al.
0

In this work, we investigate the two-step backward differentiation formula (BDF2) with nonuniform grids for the Allen-Cahn equation. We show that the nonuniform BDF2 scheme is energy stable under the time-step ratio restriction r_k:=τ_k/τ_k-1<(3+√(17))/2≈3.561. Moreover, by developing a novel kernel recombination and complementary technique, we show, for the first time, the discrete maximum principle of BDF2 scheme under the time-step ratio restriction r_k<1+√(2)≈ 2.414 and a practical time step constraint. The second-order rate of convergence in the maximum norm is also presented. Numerical experiments are provided to support the theoretical findings.

READ FULL TEXT

Authors

page 19

page 21

12/27/2021

Weighted and shifted BDF3 methods on variable grids for a parabolic problem

As is well known, the stability of the 3-step backward differentiation f...
02/10/2020

Maximum time step for the BDF3 scheme applied to gradient flows

For backward differentiation formulae (BDF) applied to gradient flows of...
01/16/2022

Unconditionally optimal error estimate of a linearized variable-time-step BDF2 scheme for nonlinear parabolic equations

In this paper we consider a linearized variable-time-step two-step backw...
02/07/2021

Mesh-robustness of the variable steps BDF2 method for the Cahn-Hilliard model

The two-step backward differential formula (BDF2) implicit method with u...
08/11/2021

Energy dissipation of Strang splitting for Allen–Cahn

We consider a class of second-order Strang splitting methods for Allen-C...
04/26/2020

Maximum Principle Preserving Schemes for Binary Systems with Long-range Interactions

We study some maximum principle preserving and energy stable schemes for...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.