190426
20180913062136.0
0036-1429
10.1137/S003614299630587X
doi
000072580500014
ISI
ARTICLE
From electrostatics to almost optimal nodal sets for polynomial interpolation in a simplex
1998
Society for Industrial and Applied Mathematics
1998
Journal Articles
The electrostatic interpretation of the Jacobi-Gauss quadrature points is exploited to obtain interpolation points suitable for approximation of smooth functions defined on a simplex. Moreover, several new estimates, based on extensive numerical studies, for approximation along the line using Jacobi-Gauss-Lobatto quadrature points as the nodal sets are presented. The electrostatic analogy is extended to the two-dimensional case, with the emphasis being on nodal sets inside a triangle for which two very good matrices of nodal sets are presented. The matrices are evaluated by computing the Lebesgue constants and they share the property that the nodes along the edges of the simplex are the Gauss-Lobatto quadrature points of the Chebyshev and Legendre polynomials, respectively. This makes the resulting nodal sets particularly well suited for integration with conventional spectral methods and supplies a new nodal basis for h - p finite element methods.
polynomial interpolation
Lebesgue constants
Jacobi polynomials
triangular elements
spectral methods
Hesthaven, Jan S.
232231
247428
655-676
2
SIAM Journal on Numerical Analysis
35
Publisher's version
355650
Publisher's version
http://infoscience.epfl.ch/record/190426/files/SIAM%20J.%20Numer.%20Anal%201998%20Hesthaven-1.pdf
MCSS
252492
U12703
oai:infoscience.tind.io:190426
article
SB
102085
EPFL-ARTICLE-190426
Hesthaven1998f/MCSS
OTHER
PUBLISHED
REVIEWED
ARTICLE