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A conservative nonlinear difference scheme for the viscous Cahn-Hilliard equation

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Abstract

Numerical solutions for the viscous Cahn-Hilliard equation are considered using the crank-Nicolson type finite difference method which conserves the mass. The corresponding stability and error analysis of the scheme are shown. The decay speeds of the solution inH 1-norm are shown. We also compare the evolution of the viscous Cahn-Hilliard equation with that of the Cahn-Hilliard equation numerically and computationally, which has been given as an open question in Novick-Cohen[13].

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Authors and Affiliations

  1. Department of Mathematics, University of Ulsan, 680-749, Ulsan, Korea

    S. M. Choo

  2. Department of Mathematics Education, Seoul National University, 151-742, Seoul, Korea

    S. K. Chung

Authors
  1. S. M. Choo
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  2. S. K. Chung
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Correspondence to S. M. Choo.

Additional information

This work was supported by Korea Research Foundation Grant (KRF-2001-002-D00036).

S. M. Choo received his degrees of B.S. and M.S. from Seoul National University. He earned his Ph.D. at Seoul National University under the direction of S.K. Chung. He has been at University of Ulsan since September, 2001. His research interest is numerical analysis.

S. K. Chung received his degrees B.S. from Seoul National University and M.S. from Sogang University. He earned his Ph.D. at The University of Texas at Arlington under the supervision of R. Kannan. He has been at Seoul National University since 1987. His research interest is numerical analysis.

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Choo, S.M., Chung, S.K. A conservative nonlinear difference scheme for the viscous Cahn-Hilliard equation. JAMC 16, 53–68 (2004). https://doi.org/10.1007/BF02936150

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