| Issue |
ESAIM: M2AN
Volume 48, Number 3, May-June 2014
|
|
|---|---|---|
| Page(s) | 697 - 726 | |
| DOI | https://doi.org/10.1051/m2an/2013126 | |
| Published online | 07 February 2014 | |
Convergence of a variational Lagrangian scheme for a nonlinear drift diffusion equation∗
Zentrum Mathematik, TU München, Boltzmannstr. 3, 85748 Garching, Germany.
matthes@ma.tum.de; osberger@ma.tum.de
Received:
29
January
2013
Revised:
2
August
2013
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.
Mathematics Subject Classification: 65N12 / 49Q20 / 65N06
Key words: Lagrangian discretization / nonlinear Fokker-Planck equation / gradient flow / Wasserstein metric
© EDP Sciences, SMAI, 2014
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