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arXiv · 1206.2859

Conservative-dissipative approximation schemes for a generalized Kramers equation

Manh Hong Duong·Mark A. Peletier·Johannes Zimmer
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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 while 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.

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Manh Hong Duong, Mark A. Peletier, Johannes Zimmer. 2012-06-13. Conservative-dissipative approximation schemes for a generalized Kramers equation. https://arxiv.org/abs/1206.2859

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