Convergence error estimates at low regularity for time discretizations of KdV

@article{Rousset2022ConvergenceEE,
  title={Convergence error estimates at low regularity for time discretizations of KdV},
  author={Frederic Rousset and Katharina Schratz},
  journal={ArXiv},
  year={2022},
  volume={abs/2102.11125}
}
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 discretisation and establish convergence error estimates at low regularity. Our analysis is based on discrete Bourgain spaces and allows to prove convergence in L for rough data u0 ∈ H , s > 0 with an explicit convergence rate. 

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