Conservative polynomial approximations and applications to Fokker-Planck equations

Laidin, Tino; Pareschi, Lorenzo

Document type :

Pré-publication ou Document de travail

Title :

Conservative polynomial approximations and applications to Fokker-Planck equations

Author(s) :

Laidin, Tino [Auteur]
Université de Lille
Reliable numerical approximations of dissipative systems [RAPSODI]
Pareschi, Lorenzo [Auteur]
Maxwell Institute for Mathematical Sciences
Department of Mathematics [Ferrara]

English keyword(s) :

Fokker-Planck equation
Galerkin spectral method
conservative methods
spectral accuracy

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

We address the problem of constructing approximations based on orthogonal polynomials that preserve an arbitrary set of moments of a given function without loosing the spectral convergence property. To this aim, we compute ...
Show more >We address the problem of constructing approximations based on orthogonal polynomials that preserve an arbitrary set of moments of a given function without loosing the spectral convergence property. To this aim, we compute the constrained polynomial of best approximation for a generic basis of orthogonal polynomials. The construction is entirely general and allows us to derive structure preserving numerical methods for partial differential equations that require the conservation of some moments of the solution, typically representing relevant physical quantities of the problem. These properties are essential to capture with high accuracy the long-time behavior of the solution. We illustrate with the aid of several numerical applications to Fokker-Planck equations the generality and the performances of the present approach.Show less >

Language :

Anglais

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Comment :

24 pages, 14 figures, 7 tables

Collections :