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

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

@Article{JCM-24-451, author = {}, 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 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 KW - Spectral method KW - 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.