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Conservative‐dissipative approximation schemes for a generalized Kramers equation
Author(s) -
Duong Manh Hong,
Peletier Mark A.,
Zimmer Johannes
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2994
Subject(s) - mathematics , dissipative system , minification , large deviations theory , mathematical optimization , statistics , physics , quantum mechanics
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 & Sons, Ltd.