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An L∞-error Estimate for the h-p Version Continuous Petrov-Galerkin Method for Nonlinear Initial 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:[email protected](L. Yi)
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Abstract

The h-p version of the continuous Petrov-Galerkin time stepping method is analyzed for nonlinear initial value problems. An L∞-error bound explicit with respect to the local discretization and regularity parameters is derived. Numerical examples are provided 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 methods 65L05: Initial value problems 65L70: Error bounds
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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