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Unconditional convergence analysis of stabilized FEM-SAV method for Cahn-Hilliard equation

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  • Li, Yaxiang
  • Wang, Jiangxing

Abstract

In this paper, we construct and analyze an energy stable scheme by combining stabilized scalar auxiliary variable (SAV) approach with finite element method (FEM) for the well-known Cahn-Hilliard equation. The unconditional energy stability and optimal error estimates of the numerical scheme are proved rigorously. Extensive numerical experiments are presented to verify our theoretical results and to demonstrate the accuracy of the proposed method.

Suggested Citation

  • Li, Yaxiang & Wang, Jiangxing, 2022. "Unconditional convergence analysis of stabilized FEM-SAV method for Cahn-Hilliard equation," Applied Mathematics and Computation, Elsevier, vol. 419(C).
    • Handle: RePEc:eee:apmaco:v:419:y:2022:i:c:s0096300321009632
    DOI: 10.1016/j.amc.2021.126880
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    References listed on IDEAS

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    1. Dehghan, Mehdi & Gharibi, Zeinab, 2021. "Numerical analysis of fully discrete energy stable weak Galerkin finite element Scheme for a coupled Cahn-Hilliard-Navier-Stokes phase-field model," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    2. Jia, Hongen & Li, Yang & Feng, Guorui & Li, Kaitai, 2020. "An efficient two-grid method for the Cahn–Hilliard equation with the concentration-dependent mobility and the logarithmic Flory-Huggins bulk potential," Applied Mathematics and Computation, Elsevier, vol. 387(C).
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    Cited by:

    1. Junxiang Yang & Yibao Li & Junseok Kim, 2022. "A Correct Benchmark Problem of a Two-Dimensional Droplet Deformation in Simple Shear Flow," Mathematics, MDPI, vol. 10(21), pages 1-10, November.

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