Canuto, C.; Quarteroni, A. Approximation results for orthogonal polynomials in Sobolev spaces. (English) Zbl 0567.41008 Math. Comput. 38, 67-86 (1982). We analyze the approximation properties of some interpolation operators and some \(L^ 2_{\omega}\)-orthogonal projection operators related to systems of polynomials which are orthonormal with respect to a weight function \(\omega (x_ 1,...,x_ d)\), \(d\geq 1\). The error estimates for the Legendre system and the Chebyshev system of the first kind are given in the norms of the Sobolev spaces \(H^ s_{\omega}\). These results are useful in the numerical analysis of the approximation of partial differential equations by spectral methods. Cited in 1 ReviewCited in 227 Documents MSC: 41A10 Approximation by polynomials 41A05 Interpolation in approximation theory Keywords:orthogonal projection operators; error estimates; Legendre system; Chebyshev system; spectral methods PDFBibTeX XMLCite \textit{C. Canuto} and \textit{A. Quarteroni}, Math. Comput. 38, 67--86 (1982; Zbl 0567.41008) Full Text: DOI