We develop a method for adaptive mesh refinement for steady state problems that arise in the numerical solution of Cahn-Hilliard equations with an obstacle free energy. The problem is discretized in time by the backward-Euler method and in space by linear finite elements. The adaptive mesh refinement is performed using residual based a posteriori estimates; the time step is adapted using a heuristic criterion. We describe the space-time adaptive algorithm and present numerical experiments in two and three space dimensions that demonstrate the usefulness of our approach. © 2007 Elsevier B.V. All rights reserved.

Adaptive finite element methods for Cahn-Hilliard equations / Banas, L.; Nürnberg, R.. - In: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. - ISSN 0377-0427. - 218:1(2008), pp. 2-11. [10.1016/j.cam.2007.04.030]

Adaptive finite element methods for Cahn-Hilliard equations

Nürnberg R.
2008

Abstract

We develop a method for adaptive mesh refinement for steady state problems that arise in the numerical solution of Cahn-Hilliard equations with an obstacle free energy. The problem is discretized in time by the backward-Euler method and in space by linear finite elements. The adaptive mesh refinement is performed using residual based a posteriori estimates; the time step is adapted using a heuristic criterion. We describe the space-time adaptive algorithm and present numerical experiments in two and three space dimensions that demonstrate the usefulness of our approach. © 2007 Elsevier B.V. All rights reserved.
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Banas, L.; Nürnberg, R.
Adaptive finite element methods for Cahn-Hilliard equations / Banas, L.; Nürnberg, R.. - In: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. - ISSN 0377-0427. - 218:1(2008), pp. 2-11. [10.1016/j.cam.2007.04.030]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/283491
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