Conservative-dissipative approximation schemes for a generalized Kramers equation

Manh Hong Duong, Mark A. Peletier, Johannes Zimmer

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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.

Original languageEnglish
Pages (from-to)2517-2540
Number of pages24
JournalMathematical Methods in the Applied Sciences
Issue number16
Early online date10 Oct 2013
Publication statusPublished - 15 Nov 2014


  • Gradient flows
  • Hamiltonian flows
  • Kramers equation
  • Optimal transport
  • Variational principle


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