Convergence error estimates at low regularity for time discretizations of KdV

02/22/2021

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by   Frédéric Rousset, et al.

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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 discretisation and establish convergence error estimates at low regularity. Our analysis is based on discrete Bourgain spaces and allows to prove convergence in L^2 for rough data u_0∈ H^s, s>0 with an explicit convergence rate.