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An L∞-error Estimate for theh-p Version Continuous Petrov-Galerkin Method for NonlinearInitial Value Problems

Part of:Numerical analysis: Ordinary differential equations

Published online by Cambridge University Press:  10 November 2015

Lijun Yi
Lijun Yi*
Affiliation:
Department of Mathematics, Shanghai Normal University, Shanghai 200234; and Division of Computational Science, E-institute of Shanghai Universities, Shanghai 200234, China
*
*Corresponding author. Email address:ylj5152@shnu.edu.cn(L.Yi)

Abstract

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The h-p version of the continuous Petrov-Galerkin time steppingmethod is analyzed for nonlinear initial value problems. AnL∞-error bound explicit with respect to the localdiscretization and regularity parameters is derived. Numerical examples areprovided to illustrate the theoretical results.

Keywords

Initial value problemsh-p versiontime stepping methodcontinuous Petrov-Galerkin methoderror bound

MSC classification

Secondary:65L60: Finite elements, Rayleigh-Ritz, Galerkin and collocation methods65L05: Initial value problems65L70: Error bounds

Information

Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 5 , Issue 4 , November 2015, pp. 301 - 311
Copyright
Copyright © Global-Science Press 2015 

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