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Discrete Approximation of the Cahn-Hilliard/Allen-Cahn system with logarithmic entropy

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Abstract

We propose a numerical scheme for the Cahn-Hilliard/Allen-Cahn system with logarithmic nonlinearity, based on the finite element method. We show its well-posedeness and convergence of the numerical solution to the weak solution of the original system. We point out some properties of a regularized numerical solution.

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Authors and Affiliations

  1. Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University, Pawińskiego 5a, 02-106, Warsaw, Poland

    Maria Gokieli

  2. Institute of Applied Mathematics, Department of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Leszek Marcinkowski

Authors
  1. Maria Gokieli
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  2. Leszek Marcinkowski
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Corresponding author

Correspondence to Maria Gokieli.

Additional information

This work was partially supported by Polish Scientific Grant 2/P03/A02116.

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Gokieli, M., Marcinkowski, L. Discrete Approximation of the Cahn-Hilliard/Allen-Cahn system with logarithmic entropy. Japan J. Indust. Appl. Math. 20, 321–351 (2003). https://doi.org/10.1007/BF03167426

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  • DOI: https://doi.org/10.1007/BF03167426

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