An energy-stable generalized-α method for the Swift–Hohenberg equation

作者：

Highlights：

• We present a second-order energy-stable time-integration method for the Swift–Hohenberg equation that suppresses numerical instabilities.

• Based on the generalized-α method, numerical dissipation is controlled via the spectral radius.

• A detailed energy-stability proof and an estimate for the stabilization parameter are provided.

• The proposed stabilization vanishes for sufficiently small time step sizes, recovering the original weak form of the equation.

• Numerical results for a pattern-formation example are used to test the convergence and energy-stability.

• We compare the primal and mixed formulation in terms of wall-clock time and approximation error.

摘要

•We present a second-order energy-stable time-integration method for the Swift–Hohenberg equation that suppresses numerical instabilities.•Based on the generalized-α method, numerical dissipation is controlled via the spectral radius.•A detailed energy-stability proof and an estimate for the stabilization parameter are provided.•The proposed stabilization vanishes for sufficiently small time step sizes, recovering the original weak form of the equation.•Numerical results for a pattern-formation example are used to test the convergence and energy-stability.•We compare the primal and mixed formulation in terms of wall-clock time and approximation error.

论文关键词：Swift–Hohenberg equation,Energy stability,Time integration,Pattern formation,Numerical instability,Numerical dissipation

论文评审过程：Received 2 April 2017, Revised 30 October 2017, Available online 15 November 2017, Version of Record 11 July 2018.

论文官网地址：https://doi.org/10.1016/j.cam.2017.11.004