A-Posteriori Error Estimation for the Legendre Spectral Galerkin Method in One-Dimension

A-Posteriori Error Estimation for the Legendre Spectral Galerkin Method in One-Dimension

Year:    2010

Numerical Mathematics: Theory, Methods and Applications, Vol. 3 (2010), Iss. 1 : pp. 40–52

Abstract

In this paper, a-posteriori error estimators are proposed for the Legendre spectral Galerkin method for  two-point boundary value problems. The key idea is to postprocess the Galerkin approximation, and the analysis shows that the postprocess improves the order of convergence. Consequently, we obtain asymptotically exact a-posteriori error estimators based on the postprocessing results. Numerical examples are included to illustrate the theoretical analysis.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2009.m9002

Numerical Mathematics: Theory, Methods and Applications, Vol. 3 (2010), Iss. 1 : pp. 40–52

Published online:    2010-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

Keywords:    Legendre spectral Galerkin method two-point boundary value problem superconvergence a-posteriori error estimation

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