Accuracy of classical conservation laws for Hamiltonian PDEs under Runge-Kutta discretizations
type: Item
instance of: scholarly article
title: Accuracy of classical conservation laws for Hamiltonian PDEs under Runge-Kutta discretizations
zbMATH Open document ID: 1167.65070
author: Jialin Hong
author: Shanshan Jiang
author: Chun Li
published in: Numerische Mathematik
publication date: 2009-05-05T00:00:00Z
review text: The authors consider the numerical behaviour of conservation laws of Hamiltonian partial differential equations in \((1+1)\) dimensions written in multi-symplectic form. They apply both for the spatial and the temporal discretisation Runge-Kutta methods and show that under certain assumptions on the coefficients of the methods a discrete local norm square conservation law holds. Then they study the accuracy of the methods providing bounds for the approximation of functions evaluated on the solution of the Hamiltonian system. Based on these results, they finally derive uniform error estimates first for the local and then also for the global discrete energy and momentum conservation laws.
reviewed by: Werner M. Seiler
Mathematics Subject Classification ID: 65P10
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 37K05
Mathematics Subject Classification ID: 37M15
Mathematics Subject Classification ID: 65L06
zbMATH DE Number: 5550619
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: conservation law
zbMATH Keywords: Runge-Kutta method
zbMATH Keywords: symplectic integrator
zbMATH Keywords: error estimates
MaRDI profile type: Publication
full work available at URL: s00211-008-0204-4
OpenAlex ID: W2061842441
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DOI: 10.1007/S00211-008-0204-4
description: scientific article; zbMATH DE number 5550619