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Convergence of linear and nonlinear Neumann–Neumann method for the Cahn–Hilliard equation

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Abstract

In this paper, we propose and analyze a non-overlapping substructuring type algorithm for the Cahn–Hilliard equation. Being a nonlinear equation, it is of great importance to develop a robust numerical method for investigating the solution behaviour of the CH equation. We present the formulation of the Neumann–Neumann method applied to the CH equation and study its convergence behaviour in one and two spatial dimension for two subdomains and also extend the method for logarithmic nonlinearity. We also present the nonlinear NN method for the CH equation. We illustrate the theoretical results by providing numerical examples.

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Acknowledgements

I wish to express my appreciation to Dr. Bankim C. Mandal for his constant support and stimulating suggestions and also like to thank the CSIR India for the financial assistance and IIT Bhubaneswar for research facility.

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  1. School of Basic Sciences, IIT Bhubaneswar, Bhubaneswar, India

    Gobinda Garai

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  1. Gobinda Garai
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Correspondence to Gobinda Garai.

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Garai, G. Convergence of linear and nonlinear Neumann–Neumann method for the Cahn–Hilliard equation. Japan J. Indust. Appl. Math. 41, 211–232 (2024). https://doi.org/10.1007/s13160-023-00600-y

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  • DOI: https://doi.org/10.1007/s13160-023-00600-y

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