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Volume 3, Issue 1
A-Posteriori Error Estimation for the Legendre Spectral Galerkin Method in One-Dimension

Lijun Yi & Benqi Guo

DOI: 10.4208/nmtma.2009.m9002

Numer. Math. Theor. Meth. Appl., 3 (2010), pp. 40-52.

Published online: 2010-03

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65N35, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-3-40, author = {Lijun Yi and Benqi Guo}, title = {A-Posteriori Error Estimation for the Legendre Spectral Galerkin Method in One-Dimension}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2010}, volume = {3}, number = {1}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2009.m9002}, url = {http://global-sci.org/intro/article_detail/nmtma/5988.html} }
TY - JOUR T1 - A-Posteriori Error Estimation for the Legendre Spectral Galerkin Method in One-Dimension AU - Lijun Yi & Benqi Guo JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 40 EP - 52 PY - 2010 DA - 2010/03 SN - 3 DO - http://doi.org/10.4208/nmtma.2009.m9002 UR - https://global-sci.org/intro/article_detail/nmtma/5988.html KW - Legendre spectral Galerkin method, two-point boundary value problem, superconvergence, a-posteriori error estimation AB -

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.

Lijun Yi and Benqi Guo. (2010). A-Posteriori Error Estimation for the Legendre Spectral Galerkin Method in One-Dimension. Numerical Mathematics: Theory, Methods and Applications. 3 (1). 40-52. doi:10.4208/nmtma.2009.m9002
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