Heida, M. (2018) Convergences of the squareroot approximation scheme to the Fokker–Planck operator. Mathematical Models and Methods in Applied Sciences, 28 (13). pp. 25992635. ISSN 02182025, ESSN: 17936314

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Official URL: https://dx.doi.org/10.1142/S0218202518500562
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 FokkerPlanck equation using a discrete notion of Gconvergence. Hence the squareroot approximation turns out to be a usefull approximation scheme to the FokkerPlanck equation in high dimensional spaces. As an example, in the special case of stationary Voronoi tessellations we use stochastic twoscale convergence to prove that this setting satisfies the Gconvergence property. In particular, the class of tessellations for which the Gconvergence result holds is not trivial.
Item Type:  Article 

Additional Information:  SFB 1114 Preprint in WIAS Preprint No. 2399: 05/2017 (http://dx.doi.org/10.20347/WIAS.PREPRINT.2399) 
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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