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Some remarks on interpolation and best approximation

Numerische Mathematik volume 137, pages 289–302 (2017)Cite this article

Abstract

Sufficient conditions are provided for establishing equivalence between best approximation error and projection/interpolation error in finite-dimensional vector spaces for general (semi)norms. The results are applied to several standard finite element spaces, modes of interpolation and (semi)norms, and a numerical study of the dependence on polynomial degree of constants appearing in our estimates is provided.

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Authors and Affiliations

  1. Department of Mathematics, University of California, San Diego, La Jolla, CA, 92093-0112, USA

    Randolph E. Bank

  2. Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR, 97201, USA

    Jeffrey S. Ovall

Authors
  1. Randolph E. Bank
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  2. Jeffrey S. Ovall
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Corresponding author

Correspondence to Jeffrey S. Ovall.

Additional information

R. E. Bank: The work of this author was supported by the National Science Foundation Under Contract DMS-1318480.

J. S. Ovall: The work of this author was supported by the National Science Foundation Under Contract DMS-1414365.

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Bank, R.E., Ovall, J.S. Some remarks on interpolation and best approximation. Numer. Math. 137, 289–302 (2017). https://doi.org/10.1007/s00211-017-0877-7

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  • DOI: https://doi.org/10.1007/s00211-017-0877-7

Mathematics Subject Classification

  • 65N30
  • 65N15
  • 65N50