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 - <p style="text-align: justify;">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. &nbsp;</p>