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Convergence of a variational Lagrangian scheme for a nonlineardrift 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 diffusionequation on an interval. The discretization is based on the equation’s gradient flowstructure with respect to the Wasserstein distance. The scheme inherits various propertiesfrom the continuous flow, like entropy monotonicity, mass preservation, metric contractionand minimum/ maximum principles. As the main result, we give a proof of convergence in thelimit of vanishing mesh size under a CFL-type condition. We also present results fromnumerical 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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