A gradient flow scheme for nonlinear fourth order equations

Düring, Bertram, Matthes, Daniel and Milišić, Josipa Pina (2010) A gradient flow scheme for nonlinear fourth order equations. Discrete and Continuous Dynamical Systems - Series B, 14 (3). pp. 935-959. ISSN 1531-3492

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We propose a method for numerical integration of Wasserstein gradient flows based on the classical minimizing movement scheme. In each time step, the discrete approximation is obtained as the solution of a constrained quadratic minimization problem on a finite-dimensional function space. Our method is applied to the nonlinear fourth-order Derrida-Lebowitz-Speer-Spohn equation, which arises in quantum semiconductor theory. We prove well-posedness of the scheme and derive a priori estimates on the discrete solution. Furthermore, we present numerical results which indicate second-order convergence and unconditional stability of our scheme. Finally, we compare these results to those obtained from different semi- and fully implicit finite difference discretizations.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Bertram During
Date Deposited: 06 Feb 2012 19:14
Last Modified: 13 Jun 2012 14:58
URI: http://sro.sussex.ac.uk/id/eprint/19666
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