Abstract
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 language | English |
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Pages (from-to) | 2517-2540 |
Number of pages | 24 |
Journal | Mathematical Methods in the Applied Sciences |
Volume | 37 |
Issue number | 16 |
Early online date | 10 Oct 2013 |
DOIs | |
Publication status | Published - 15 Nov 2014 |
Keywords
- Gradient flows
- Hamiltonian flows
- Kramers equation
- Optimal transport
- Variational principle