Numerical hypocoercivity for the Kolmogorov equation

Porretta A, Zuazua E (2017)

Publication Type: Journal article

Publication year: 2017

Journal

Mathematics of Computation American Mathematical Society

Book Volume: 86

Pages Range: 97-119

Journal Issue: 303

DOI: 10.1090/mcom/3157

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 ( → ∞, 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 L2- norms of solutions and partial derivatives, which are of different order because of the anisotropy of the model.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

Università degli Studi di Roma 'Tor Vergata' IT Italy (IT) Universidad Autónoma de Madrid (UAM) ES Spain (ES)

How to cite

APA:

Porretta, A., & Zuazua, E. (2017). Numerical hypocoercivity for the Kolmogorov equation. Mathematics of Computation, 86(303), 97-119. https://dx.doi.org/10.1090/mcom/3157

MLA:

Porretta, Alessio, and Enrique Zuazua. "Numerical hypocoercivity for the Kolmogorov equation." Mathematics of Computation 86.303 (2017): 97-119.

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