Repository: Freie Universit├Ąt Berlin, Math Department

On Convergences of square-root approximation scheme to Fokker--Planck operator

Heida, M. (2017) On Convergences of square-root approximation scheme to Fokker--Planck operator. SFB 1114 Preprint at WIAS 05/2017 . pp. 1-30. (Unpublished)

[img]
Preview
PDF
518kB

Abstract

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
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
ID Code:2211
Deposited By: Silvia Hoemke
Deposited On:15 Feb 2018 15:37
Last Modified:15 Feb 2018 15:37

Repository Staff Only: item control page