On the rate of convergence of a numerical scheme for Fractional conservation laws with noise - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue IMA Journal of Numerical Analysis Année : 2023

On the rate of convergence of a numerical scheme for Fractional conservation laws with noise

Ujjwal Koley
  • Fonction : Auteur

Résumé

Abstract We consider a semidiscrete finite volume scheme for a degenerate fractional conservation law driven by a cylindrical Wiener process. Making use of the bounded variation (BV) estimates, and a clever adaptation of classical Kružkov theory, we provide estimates on the rate of convergence for approximate solutions to degenerate fractional problems. The main difficulty stems from the degenerate fractional operator and requires a significant departure from the existing strategy to establish Kato’s type of inequality. Indeed, recasting the mathematical framework recently developed in Bhauryal et al. (2021, J. Differential Equations, 284, 433–521), we establish such Kato’s type of inequality for a finite volume scheme. Finally, as an application of this theory, we demonstrate numerical convergence rates.

Dates et versions

hal-04286164 , version 1 (15-11-2023)

Identifiants

Citer

Ujjwal Koley, Guy Vallet. On the rate of convergence of a numerical scheme for Fractional conservation laws with noise. IMA Journal of Numerical Analysis, 2023, ⟨10.1093/imanum/drad015⟩. ⟨hal-04286164⟩
5 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More