Volume 7, Issue 2
The a Posteriori Error Estimates for Chebyshev-Galerkin Spectral Methods in One Dimension

Adv. Appl. Math. Mech., 7 (2015), pp. 145-157.

Published online: 2018-05

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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.

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@Article{AAMM-7-145, author = {}, title = {The a Posteriori Error Estimates for Chebyshev-Galerkin Spectral Methods in One Dimension}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {7}, number = {2}, pages = {145--157}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m193}, url = {http://global-sci.org/intro/article_detail/aamm/12041.html} }
TY - JOUR T1 - The a Posteriori Error Estimates for Chebyshev-Galerkin Spectral Methods in One Dimension JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 145 EP - 157 PY - 2018 DA - 2018/05 SN - 7 DO - http://doi.org/10.4208/aamm.2013.m193 UR - https://global-sci.org/intro/article_detail/aamm/12041.html KW - AB -

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.

Jianwei Zhou. (1970). The a Posteriori Error Estimates for Chebyshev-Galerkin Spectral Methods in One Dimension. Advances in Applied Mathematics and Mechanics. 7 (2). 145-157. doi:10.4208/aamm.2013.m193
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