Contributions to Books:

B. Düring, D. Matthes, J. Milisic:
"A gradient flow scheme for nonlinear fourth order equations";
in: "ASC Report 25/2009", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2009, ISBN: 978-3-902627-02-5.

English abstract:
We propose a method for numerical integration ofWasserstein 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 wellposedness
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

Electronic version of the publication:

Related Projects:
Project Head Ansgar Jüngel:
Numerik und Modellierung nichtlinearer partieller Differentialgleichungen zur Beschreibung von Kredit- und Preisrisiken

Created from the Publication Database of the Vienna University of Technology.