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A comparison of interpolation grids over the triangle or the tetrahedron

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Abstract

A simple strategy for constructing a sequence of increasingly refined interpolation grids over the triangle or the tetrahedron is discussed with the goal of achieving uniform convergence and ensuring high interpolation accuracy. The interpolation nodes are generated based on a one-dimensional master grid comprised of the zeros of the Lobatto, Legendre, Chebyshev, and second-kind Chebyshev polynomials. Numerical computations show that the Lebesgue constant and interpolation accuracy of some proposed grids compare favorably with those of alternative grids constructed by optimization, including the Fekete set. While some sets are clearly preferable to others, no single set can claim uniformly better convergence properties as the number of nodes is raised.

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Authors and Affiliations

  1. School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, England, UK

    M. G. Blyth

  2. Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA, 92093-0411, USA

    H. Luo & C. Pozrikidis

Authors
  1. M. G. Blyth
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  2. H. Luo
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  3. C. Pozrikidis
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Correspondence to M. G. Blyth.

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Blyth, M.G., Luo, H. & Pozrikidis, C. A comparison of interpolation grids over the triangle or the tetrahedron. J Eng Math 56, 263–272 (2006). https://doi.org/10.1007/s10665-006-9063-0

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  • DOI: https://doi.org/10.1007/s10665-006-9063-0

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