Convergence error estimates at low regularity for time discretizations of KdV

2021/02/22 by Frédéric Rousset, Katharina Schratz, Rousset, Frédéric +1 · 1 citation
Mathematics · Engineering · #Numerical methods for differential equations #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods

paper · doi:10.48550/arxiv.2102.11125

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 discretisation and establish convergence error estimates at low regularity. Our analysis is based on discrete Bourgain spaces and allows to prove convergence in L² for rough data u₀ ∈ H^s, s>0 with an explicit convergence rate.

Cited by

• Computing rough solutions of the KdV equation below \bf L²

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