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 $u_{0} \in H^s,$ $s>0$ with an explicit convergence rate.

中文翻译：

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KdV时间离散的低规则收敛误差估计

我们考虑周期性Korteweg-de Vries方程的各种滤波时间离散化：滤波指数积分器，滤波Lie分裂方案以及基于滤波共振的离散化，并以低规则性建立收敛误差估计。我们的分析基于离散的Bourgain空间，并允许证明$ L ^ 2 $的粗糙数据$ u_ {0} \ in H ^ s，$ $ s> 0 $具有收敛速度。