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B. Düring, D. Matthes, J. Milisic:
"A gradient flow scheme for nonlinear fourth order equations";
Discrete and Continuous Dynamical Systems B, 14 (2010), 3; S. 935 - 959.

s. engl. Abstract

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.

Wasserstein gradient flow, higher-order diffusion equation, numerical solution

http://dx.doi.org/10.3934/dcdsb.2010.14.935

Projektleitung Bertram Düring:
Kinetische Vermögensverteilungsmodelle und diffusive Grenzwert-Gleichungen

Projektleitung Ansgar Jüngel:
Numerik und Modellierung nichtlinearer partieller Differentialgleichungen zur Beschreibung von Kredit- und Preisrisiken