Volume 52, Number 3, May–June 2018
|Page(s)||1051 - 1083|
|Published online||13 September 2018|
Spectral methods for Langevin dynamics and associated error estimates
Université Paris-Est, CERMICS (ENPC), Inria,
* Corresponding author: firstname.lastname@example.org
Accepted: 23 August 2017
We prove the consistency of Galerkin methods to solve Poisson equations where the differential operator under consideration is hypocoercive. We show in particular how the hypocoercive nature of the generator associated with Langevin dynamics can be used at the discrete level to first prove the invertibility of the rigidity matrix, and next provide error bounds on the approximation of the solution of the Poisson equation. We present general convergence results in an abstract setting, as well as explicit convergence rates for a simple example discretized using a tensor basis. Our theoretical findings are illustrated by numerical simulations.
Mathematics Subject Classification: 82C31 / 35H10 / 65N15 / 65N35
Key words: Langevin dynamics / spectral methods / Poisson equation / error estimates.
© EDP Sciences, SMAI 2018
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