Conservative‐dissipative approximation schemes for a generalized Kramers equation. (10th October 2013)

• Record Type: Journal Article
• Authors: Duong, Manh Hong; Peletier, Mark A.; Zimmer, Johannes
• Is Part Of: Mathematical methods in the applied sciences. Volume 37:Number 16(2014:Nov. 15)
• Page Start: 2517
• Page End: 2540
• Publication Date: 2013-10-10
• Subjects: Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.2994
• Languages: English
• ISSNs: 0170-4214

Abstract

<abstract abstract-type="main" id="mma2994-abs-0001"> <title> <x xml:space="preserve">Abstract</x> </title> <p id="mma2994-para-0001">We propose three new discrete variational schemes that capture the conservative‐dissipative structure of a generalized Kramers equation. The first two schemes are single‐step minimization schemes, whereas the third one combines a streaming and a minimization step. The cost functionals in the schemes are inspired by the rate functional in the Freidlin‐Wentzell theory of large deviations for the underlying stochastic system. We prove that all three schemes converge to the solution of the generalized Kramers equation. Copyright © 2013 John Wiley &amp; Sons, Ltd.</p> </abstract>