Conservative-dissipative approximation schemes for a generalized Kramers equation

Manh Hong Duong, Mark A. Peletier, Johannes Zimmer

OAI: oai:purehost.bath.ac.uk:openaire_cris_publications/13ad8e55-a6b5-47a4-845e-f99bd838832f • DOI: https://doi.org/10.1002/mma.2994

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.

Gradient flows Hamiltonian flows Kramers equation Optimal transport Variational principle