Convergence error estimates at low regularity for time discretizations of KdV

02/22/2021
by   Frédéric Rousset, et al.
0

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.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

12/28/2020

Error estimates at low regularity of splitting schemes for NLS

We study a filtered Lie splitting scheme for the cubic nonlinear Schrödi...
06/23/2020

Fourier integrator for periodic NLS: low regularity estimates via discrete Bourgain spaces

In this paper, we propose a new scheme for the integration of the period...
01/31/2022

Error analysis of a class of semi-discrete schemes for solving the Gross-Pitaevskii equation at low regularity

We analyse a class of time discretizations for solving the Gross-Pitaevs...
06/19/2022

An unfiltered low-regularity integrator for the KdV equation with solutions below H^1

This article is concerned with the construction and analysis of new time...
12/19/2021

Explicit Numerical Methods for High Dimensional Stochastic Nonlinear Schrödinger Equation: Divergence, Regularity and Convergence

This paper focuses on the construction and analysis of explicit numerica...
01/25/2022

Error estimates for a finite volume scheme for advection-diffusion equations with rough coefficients

We study the implicit upwind finite volume scheme for numerically approx...
01/06/2022

Numerical analysis of several FFT-based schemes for computational homogenization

We study the convergences of several FFT-based schemes that are widely a...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.