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Volume 24, Issue 4
Chebyshev Weighted Norm Least-Squares Spectral Methods for the Elliptic Problem

Sang Dong Kim & Byeong Chun Shin

J. Comp. Math., 24 (2006), pp. 451-462.

Published online: 2006-08

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  • Abstract

We develop and analyze a first-order system least-squares spectral method for the second-order elliptic boundary value problem with variable coefficients. We first analyze the Chebyshev weighted norm least-squares functional defined by the sum of the $L^2_w$- and $H^{-1}_w$-norm of the residual equations and then we replace the negative norm by the discrete negative norm and analyze the discrete Chebyshev weighted least-squares method. The spectral convergence is derived for the proposed method. We also present various numerical experiments. The Legendre weighted least-squares method can be easily developed by following this paper.  

  • Keywords

Least-squares methods, Spectral method, Negative norm.

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COPYRIGHT: © Global Science Press

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@Article{JCM-24-451, author = {Sang Dong Kim and Byeong Chun Shin}, title = {Chebyshev Weighted Norm Least-Squares Spectral Methods for the Elliptic Problem}, journal = {Journal of Computational Mathematics}, year = {2006}, volume = {24}, number = {4}, pages = {451--462}, abstract = {

We develop and analyze a first-order system least-squares spectral method for the second-order elliptic boundary value problem with variable coefficients. We first analyze the Chebyshev weighted norm least-squares functional defined by the sum of the $L^2_w$- and $H^{-1}_w$-norm of the residual equations and then we replace the negative norm by the discrete negative norm and analyze the discrete Chebyshev weighted least-squares method. The spectral convergence is derived for the proposed method. We also present various numerical experiments. The Legendre weighted least-squares method can be easily developed by following this paper.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8766.html} }
TY - JOUR T1 - Chebyshev Weighted Norm Least-Squares Spectral Methods for the Elliptic Problem AU - Sang Dong Kim & Byeong Chun Shin JO - Journal of Computational Mathematics VL - 4 SP - 451 EP - 462 PY - 2006 DA - 2006/08 SN - 24 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8766.html KW - Least-squares methods, Spectral method, Negative norm. AB -

We develop and analyze a first-order system least-squares spectral method for the second-order elliptic boundary value problem with variable coefficients. We first analyze the Chebyshev weighted norm least-squares functional defined by the sum of the $L^2_w$- and $H^{-1}_w$-norm of the residual equations and then we replace the negative norm by the discrete negative norm and analyze the discrete Chebyshev weighted least-squares method. The spectral convergence is derived for the proposed method. We also present various numerical experiments. The Legendre weighted least-squares method can be easily developed by following this paper.  

Sang Dong Kim and Byeong Chun Shin. (2006). Chebyshev Weighted Norm Least-Squares Spectral Methods for the Elliptic Problem. Journal of Computational Mathematics. 24 (4). 451-462. doi:
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