Vol. 4, No. 1, 2022
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Convergence error estimates at low regularity for time discretizations of KdV

Frédéric Rousset and Katharina Schratz
Vol. 4 (2022), No. 1, 127–152
DOI: 10.2140/paa.2022.4.127
Abstract

We consider various filtered time discretizations of the periodic Korteweg–de Vries equation: a filtered exponential integrator, a filtered Lie splitting scheme, as well as a filtered resonance-based discretization, and establish error estimates at low regularity. Our analysis is based on discrete Bourgain spaces and allows us to prove convergence in L2 for rough data u0 ∈ Hs , s > 0, with an explicit convergence rate.

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Keywords
discrete Bourgain spaces, error estimates at low regularity, Korteweg–de Vries equation
Mathematical Subject Classification
Primary: 65M15
Milestones
Received: 25 April 2021
Revised: 6 October 2021
Accepted: 14 November 2021
Published: 29 April 2022
Authors
Frédéric Rousset
Université Paris-Saclay
CNRS, Laboratoire de Mathématiques d’Orsay (UMR 8628)
Orsay
France
Katharina Schratz
Laboratoire Jacques-Louis Lions (UMR 7598)
Sorbonne Université, UPMC
Paris
France