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The a Posteriori Error Estimates for Chebyshev-Galerkin Spectral Methods in One Dimension

Published online by Cambridge University Press:  23 March 2015

Jianwei Zhou
Jianwei Zhou*
Affiliation:
Department of Mathematics, Linyi University, Shandong 276005, China
*
*Corresponding author. Email: jwzhou@yahoo.com (J. W. Zhou)
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Abstract

In this paper, the Chebyshev-Galerkin spectral approximations are employed to investigate Poisson equations and the fourth order equations in one dimension. Meanwhile, p-version finite element methods with Chebyshev polynomials are utilized to solve Poisson equations. The efficient and reliable a posteriori error estimators are given for different models. Furthermore, the a priori error estimators are derived independently. Some numerical experiments are performed to verify the theoretical analysis for the a posteriori error indicators and a priori error estimations.

Keywords

65N3065N3565M70Chebyshev-Galerkin spectral approximationChebyshev polynomiala posteriori error indicatorp-version finite element method
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 2 , April 2015 , pp. 145 - 157
Copyright
Copyright © Global-Science Press 2015 

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