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

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 appearing in diblock co-polymer phase separation, tumor growth, image inpainting and segmentation.

27 pages, 6 figures. Published in Journal of Numerical Mathematics

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Cited by in corpus (2)

• Strong error estimates for a fully discrete SAV scheme for the stochastic Allen--Cahn equation with multiplicative noise
• A convergent stochastic scalar auxiliary variable method