Linear and energy stable schemes for the Swift–Hohenberg equation with quadratic-cubic nonlinearity based on a modified scalar auxiliary variable approach

Junxiang Yang, Junseok Kim

Research output: Contribution to journalArticlepeer-review

Abstract

In this study, we develop linear and energy stable numerical schemes for the Swift–Hohenberg equation with quadratic-cubic nonlinearity. A modified scalar auxiliary variable (SAV) approach is used to construct the temporally first- and second-order accurate discretizations. Different from the classical SAV approach, the proposed schemes permit us to solve the governing equations in a step-by-step manner, i.e., the calculation of inner product is not needed. We analytically prove the energy stability. We solve the resulting system of discrete equations using the linear multigrid method. We perform various numerical examples to show the accuracy and energy stability of the proposed method. The pattern formations in two- and three-dimensional spaces are also simulated.

Original languageEnglish
Article number21
JournalJournal of Engineering Mathematics
Volume128
Issue number1
DOIs
Publication statusPublished - 2021 Jun

Keywords

  • Energy stability
  • Pattern formation
  • SAV approach
  • Swift–Hohenberg equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

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