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A gradient flow scheme for nonlinear fourth order equations

journal contribution
posted on 2023-06-07, 22:16 authored by Bertram Duering, Daniel Matthes, Josipa Pina Milišic
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.

History

Publication status

  • Published

Journal

Discrete and Continuous Dynamical Systems - Series B

ISSN

1531-3492

Publisher

American Institute of Mathematical Sciences

Issue

3

Volume

14

Page range

935-959

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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