Conservative polynomial approximations and applications to Fokker-Planck equations - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

Conservative polynomial approximations and applications to Fokker-Planck equations

Résumé

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.
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Dates et versions

hal-04449712 , version 1 (09-02-2024)

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  • HAL Id : hal-04449712 , version 1

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Tino Laidin, Lorenzo Pareschi. Conservative polynomial approximations and applications to Fokker-Planck equations. 2024. ⟨hal-04449712⟩
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