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Convergence of a variational Lagrangian scheme for a nonlinear drift diffusion equation∗

Published online by Cambridge University Press:  07 February 2014

Daniel Matthes  and
Horst Osberger
Daniel Matthes
Affiliation:
Zentrum Mathematik, TU München, Boltzmannstr. 3, 85748 Garching, Germany.. matthes@ma.tum.de; osberger@ma.tum.de
Horst Osberger
Affiliation:
Zentrum Mathematik, TU München, Boltzmannstr. 3, 85748 Garching, Germany.. matthes@ma.tum.de; osberger@ma.tum.de
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Abstract

We study a Lagrangian numerical scheme for solution of a nonlinear drift diffusion equation on an interval. The discretization is based on the equation’s gradient flow structure with respect to the Wasserstein distance. The scheme inherits various properties from the continuous flow, like entropy monotonicity, mass preservation, metric contraction and minimum/ maximum principles. As the main result, we give a proof of convergence in the limit of vanishing mesh size under a CFL-type condition. We also present results from numerical experiments.

Keywords

Lagrangian discretizationnonlinear Fokker-Planck equationgradient flowWasserstein metric
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 3 , May 2014 , pp. 697 - 726
Copyright
© EDP Sciences, SMAI, 2014

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