Convergence of a variational lagrangian scheme for a nonlinear drift diffusion equation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 3, p. 697-726
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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.

DOI : https://doi.org/10.1051/m2an/2013126
Classification:  65N12,  49Q20,  65N06
Keywords: lagrangian discretization, nonlinear Fokker-Planck equation, gradient flow, Wasserstein metric
@article{M2AN_2014__48_3_697_0,
     author = {Matthes, Daniel and Osberger, Horst},
     title = {Convergence of a variational lagrangian scheme for a nonlinear drift diffusion equation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {3},
     year = {2014},
     pages = {697-726},
     doi = {10.1051/m2an/2013126},
     zbl = {1293.65119},
     mrnumber = {3177862},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2014__48_3_697_0}
}
Matthes, Daniel; Osberger, Horst. Convergence of a variational lagrangian scheme for a nonlinear drift diffusion equation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 3, pp. 697-726. doi : 10.1051/m2an/2013126. http://www.numdam.org/item/M2AN_2014__48_3_697_0/

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