Over the rectangle Ω = (−1. 1) × (−π, π) of R2, interpolation involving algebraic polynomials of degree M in the x direction, and trigonometric polynomials of degree N in the y direction is analyzed. The interpolation nodes are Cartesian products of the Chebyshev points View the MathML source, and the equispaced points View the MathML source. This interpolation process is the basis of those spectral collocation methods using Fourier and Chebyshev expansions at the same time. For the convergence analysis of these methods, an estimate of the L2-norm of the interpolation error is needed. In this paper, it is shown that this error decays like N−r + Ms provided the interpolation function belongs to the non-isotropic Sobolev space Hr,s(Ω). ☆ This research has been sponsored in part by the U.S. Army through its European Research Office under Contract DAJA-84-C-0035. Copyright © 1987 Published by Elsevier Inc.
Blending Fourier and Chebyshev interpolation
QUARTERONI, ALFIO MARIA
1987-01-01
Abstract
Over the rectangle Ω = (−1. 1) × (−π, π) of R2, interpolation involving algebraic polynomials of degree M in the x direction, and trigonometric polynomials of degree N in the y direction is analyzed. The interpolation nodes are Cartesian products of the Chebyshev points View the MathML source, and the equispaced points View the MathML source. This interpolation process is the basis of those spectral collocation methods using Fourier and Chebyshev expansions at the same time. For the convergence analysis of these methods, an estimate of the L2-norm of the interpolation error is needed. In this paper, it is shown that this error decays like N−r + Ms provided the interpolation function belongs to the non-isotropic Sobolev space Hr,s(Ω). ☆ This research has been sponsored in part by the U.S. Army through its European Research Office under Contract DAJA-84-C-0035. Copyright © 1987 Published by Elsevier Inc.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
