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Numerical analysis of a Cahn–Hilliard type equation with dynamic boundary conditions

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Abstract

We study space and time discretizations of a Cahn–Hilliard type equation with dynamic boundary conditions. We first study a semi-discrete version of the equation and we prove optimal error estimates in energy norms and weaker norms. Then, we study the stability of the fully discrete scheme obtained by applying the Euler backward scheme to the space semi-discrete problem. In particular, we show that this fully discrete problem is unconditionally stable. Some numerical results in two space dimensions conclude the paper.

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Authors and Affiliations

  1. Laboratoire de Mathématiques et Applications, UMR 7348 CNRS, Université de Poitiers, SP2MI Boulevard Marie et Pierre Curie, Téléport 2 BP30179, 86962 , Futuroscope Chasseneuil Cedex, France

    Haydi Israel, Alain Miranville & Madalina Petcu

  2. Institute of Mathematics of the Romanian Academy, Bucharest, Romania

    Madalina Petcu

Authors
  1. Haydi Israel
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  2. Alain Miranville
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  3. Madalina Petcu
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Correspondence to Alain Miranville.

Additional information

Communicated by Salvatore Rionero.

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Israel, H., Miranville, A. & Petcu, M. Numerical analysis of a Cahn–Hilliard type equation with dynamic boundary conditions. Ricerche mat. 64, 25–50 (2015). https://doi.org/10.1007/s11587-014-0187-7

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  • DOI: https://doi.org/10.1007/s11587-014-0187-7

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