A multigrid method for the Cahn–Hilliard equation with obstacle potential

Banas L, Nürnberg R (2009)
Applied Mathematics and Computation 213(2): 290-303.

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We present a multigrid finite element method for the deep quench obstacle Cahn–Hilliard equation. The non-smooth nature of this highly nonlinear fourth order partial differential equation make this problem particularly challenging. The method exhibits mesh-independent convergence properties in practice for arbitrary time step sizes. In addition, numerical evidence shows that this behaviour extends to small values of the interfacial parameter . Several numerical examples are given, including comparisons with existing alternative solution methods for the Cahn–Hilliard equation.
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Banas L, Nürnberg R. A multigrid method for the Cahn–Hilliard equation with obstacle potential. Applied Mathematics and Computation. 2009;213(2):290-303.
Banas, L., & Nürnberg, R. (2009). A multigrid method for the Cahn–Hilliard equation with obstacle potential. Applied Mathematics and Computation, 213(2), 290-303. doi:10.1016/j.amc.2009.03.036
Banas, L., and Nürnberg, R. (2009). A multigrid method for the Cahn–Hilliard equation with obstacle potential. Applied Mathematics and Computation 213, 290-303.
Banas, L., & Nürnberg, R., 2009. A multigrid method for the Cahn–Hilliard equation with obstacle potential. Applied Mathematics and Computation, 213(2), p 290-303.
L. Banas and R. Nürnberg, “A multigrid method for the Cahn–Hilliard equation with obstacle potential”, Applied Mathematics and Computation, vol. 213, 2009, pp. 290-303.
Banas, L., Nürnberg, R.: A multigrid method for the Cahn–Hilliard equation with obstacle potential. Applied Mathematics and Computation. 213, 290-303 (2009).
Banas, Lubomir, and Nürnberg, Robert. “A multigrid method for the Cahn–Hilliard equation with obstacle potential”. Applied Mathematics and Computation 213.2 (2009): 290-303.
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