Repository: Freie Universität Berlin, Math Department

Convergences of the squareroot approximation scheme to the Fokker–Planck operator

Heida, M. (2018) Convergences of the squareroot approximation scheme to the Fokker–Planck operator. Mathematical Models and Methods in Applied Sciences, 28 (13). pp. 2599-2635. ISSN 0218-2025, ESSN: 1793-6314


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We study the qualitative convergence properties of a finite volume scheme that recently was proposed by Lie, Fackeldey and Weber [SIAM Journal on Matrix Analysis and Applications 2013 (34/2)] in the context of conformation dynamics. The scheme was derived from physical principles and is called the squareroot approximation (SQRA) scheme. We show that solutions to the SQRA equation converge to solutions of the Fokker-Planck equation using a discrete notion of G-convergence. Hence the squareroot approximation turns out to be a usefull approximation scheme to the Fokker-Planck equation in high dimensional spaces. As an example, in the special case of stationary Voronoi tessellations we use stochastic two-scale convergence to prove that this setting satisfies the G-convergence property. In particular, the class of tessellations for which the G-convergence result holds is not trivial.

Item Type:Article
Additional Information:SFB 1114 Preprint in WIAS Preprint No. 2399: 05/2017 (
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
ID Code:2211
Deposited By: Silvia Hoemke
Deposited On:15 Feb 2018 15:37
Last Modified:04 Jun 2019 16:23

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