Geodesic
Spectral methods for Langevin dynamics and associated error estimates
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 3, pp. 1051-1083

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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.

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DOI : 10.1051/m2an/2017044
Classification : 82C31, 35H10, 65N15, 65N35
Keywords: Langevin dynamics, spectral methods, Poisson equation, error estimates.

Roussel, Julien 1 ; Stoltz, Gabriel 1

1 
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     title = {Spectral methods for {Langevin} dynamics and associated error estimates},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1051--1083},
     publisher = {EDP-Sciences},
     volume = {52},
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     year = {2018},
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Roussel, Julien; Stoltz, Gabriel. Spectral methods for Langevin dynamics and associated error estimates. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 3, pp. 1051-1083. doi: 10.1051/m2an/2017044

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