Stability and convergence of relaxed scalar auxiliary variable schemes for Cahn-Hilliard systems with bounded mass source
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913651374424064 |
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| author | Lam, Kei Fong Wang, Ru |
| author_facet | Lam, Kei Fong Wang, Ru |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_08543 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability and convergence of relaxed scalar auxiliary variable schemes for Cahn-Hilliard systems with bounded mass source Lam, Kei Fong Wang, Ru Numerical Analysis 35K35, 35K55, 65M12, 65Z05 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. |
| title | Stability and convergence of relaxed scalar auxiliary variable schemes for Cahn-Hilliard systems with bounded mass source |
| topic | Numerical Analysis 35K35, 35K55, 65M12, 65Z05 |
| url | https://arxiv.org/abs/2501.08543 |