Year: 2006
Journal of Computational Mathematics, Vol. 24 (2006), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2006-JCM-8766
Journal of Computational Mathematics, Vol. 24 (2006), Iss. 4 : pp. 451–462
Published online: 2006-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Least-squares methods Spectral method Negative norm.