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Convergence error
estimates at low regularity for time discretizations of
KdV
Frédéric Rousset and Katharina Schratz |
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Vol. 4 (2022), No. 1, 127–152
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Abstract |
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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 for rough data , , with an explicit convergence rate. |
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Keywords
discrete Bourgain spaces, error estimates at low
regularity, Korteweg–de Vries equation
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Mathematical Subject Classification
Primary: 65M15
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Milestones
Received: 25 April 2021
Revised: 6 October 2021
Accepted: 14 November 2021
Published: 29 April 2022
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Authors |
| Frédéric Rousset | |
| Université Paris-Saclay CNRS, Laboratoire de Mathématiques d’Orsay (UMR 8628) Orsay France |
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| Katharina Schratz | |
| Laboratoire Jacques-Louis Lions (UMR
7598) Sorbonne Université, UPMC Paris France |
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