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A stable, convergent, conservative and linear finite difference scheme for the Cahn-Hilliard equation

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Abstract

We propose a stable, convergent, conservative and linear finite difference scheme to solve numerically the Cahn-Hilliard equation. The proposed scheme realizes both linearity and stability. We show uniqueness, existence and convergence of the solution to the scheme. Numerical examples demonstrate the effectiveness of the proposed scheme.

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Authors and Affiliations

  1. Cybermedia Center, Osaka University, 560-0043, Osaka, Japan

    Daisuke Furihata

  2. Department of Computational Science and Engineering, Nagoya University, 464-8603, Nagoya, Japan

    Takayasu Matsuo

Authors
  1. Daisuke Furihata
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  2. Takayasu Matsuo
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Correspondence to Daisuke Furihata.

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Furihata, D., Matsuo, T. A stable, convergent, conservative and linear finite difference scheme for the Cahn-Hilliard equation. Japan J. Indust. Appl. Math. 20, 65 (2003). https://doi.org/10.1007/BF03167463

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  • DOI: https://doi.org/10.1007/BF03167463

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