A new Lagrange multiplier approach for gradient flows: A new Lagrange multiplier approach

Qing Cheng, Chun Liu, Jie Shen

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

We propose a new Lagrange multiplier approach to design unconditional energy stable schemes for gradient flows. The new approach leads to unconditionally energy stable schemes that are as accurate and efficient as the recently proposed SAV approach (Shen, Xu, and Yang 2018), but enjoys two additional advantages: (i) schemes based on the new approach dissipate the original energy, as opposed to a modified energy in the recently proposed SAV approach (Shen, Xu, and Yang 2018);and (ii) they do not require the nonlinear part of the free energy to be bounded from below as is required in the SAV approach. The price we pay for these advantages is that a nonlinear algebraic equation has to be solved to determine the Lagrange multiplier. We present ample numerical results to validate the new approach, and, as a particular example of challenging applications, we consider a block copolymer (BCP)/coupled Cahn–Hilliard model, and carry out new and nontrivial simulations which are consistent with experiment results.

Original languageEnglish (US)
Article number113070
JournalComputer Methods in Applied Mechanics and Engineering
Volume367
DOIs
StatePublished - Aug 1 2020

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

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