Stability and convergence of relaxed scalar auxiliary variable schemes for Cahn-Hilliard systems with bounded mass source

Kei Fong Lam*, Ru Wang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

Abstract

The scalar auxiliary variable (SAV) approach of Shen et al. (2018), which presents a novel way to discretize a large class of gradient flows, has been extended and improved by many authors for general dissipative systems. In this work we consider a Cahn-Hilliard system with mass source that, for image processing and biological applications, may not admit a dissipative structure involving the Ginzburg-Landau energy. Hence, compared to previous works, the stability of SAV-discrete solutions for such systems is not immediate. We establish, with a bounded mass source, stability and convergence of time discrete solutions for a first-order relaxed SAV scheme in the sense of Jiang et al. (2022), and apply our ideas to Cahn-Hilliard systems with mass source appearing in diblock co-polymer phase separation, tumor growth, image inpainting and segmentation.

Original languageEnglish
JournalJournal of Numerical Mathematics
DOIs
Publication statusPublished - 30 Aug 2023

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics

User-Defined Keywords

  • Cahn-Hilliard equation
  • convergence analysis
  • energy stability
  • mass source
  • Scalar auxiliary variable

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