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Mathematics of Computation

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Approximation results for orthogonal polynomials in Sobolev spaces


Authors: C. Canuto and A. Quarteroni
Journal: Math. Comp. 38 (1982), 67-86
MSC: Primary 41A10
DOI: https://doi.org/10.1090/S0025-5718-1982-0637287-3
MathSciNet review: 637287
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Abstract: We analyze the approximation properties of some interpolation operators and some $ L_\omega ^2$-orthogonal projection operators related to systems of polynomials which are orthonormal with respect to a weight function $ \omega ({x_1}, \ldots ,{x_d})$, $ d \geqslant 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_\omega ^s$. These results are useful in the numerical analysis of the approximation of partial differential equations by spectral methods.


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DOI: https://doi.org/10.1090/S0025-5718-1982-0637287-3
Article copyright: © Copyright 1982 American Mathematical Society