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- W2317502341 abstract "We prove that a finite-difference centered approximation for the Kolmogorov equation in the whole space preserves the decay properties of continuous solutions as $t to infty$, independently of the mesh-size parameters. This is a manifestation of the property of numerical hypo-coercivity, and it holds both for semi-discrete and fully discrete approximations. The method of proof is based on the energy methods developed by Herau and Villani, employing well-balanced Lyapunov functionals mixing different energies, suitably weighted and equilibrated by multiplicative powers in time. The decreasing character of this Lyapunov functional leads to the optimal decay of the $L^2$-norms of solutions and partial derivatives, which are of different order because of the anisotropy of the model." @default.
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- W2317502341 date "2016-05-25" @default.
- W2317502341 modified "2023-10-06" @default.
- W2317502341 title "Numerical hypocoercivity for the Kolmogorov equation" @default.
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- W2317502341 doi "https://doi.org/10.1090/mcom/3157" @default.
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