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A Lagrange Interpolation Method by Trivariate Cubic C 1 Splines of Low Locality

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Book cover Approximation Theory XIII: San Antonio 2010

Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 13))

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Abstract

We develop a local Lagrange interpolation method for trivariate cubic C 1 splines. The splines are constructed on a uniform partition consisting of octahedra (with one additional edge) and tetrahedra. The method is 2-local and stable and therefore yields optimal approximation order. The numerical results and visualizations confirm the efficiency of the method.

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Author information

Authors and Affiliations

  1. University of Mannheim, Mannheim, Germany

    G. Nürnberger & G. Schneider

Authors
  1. G. Nürnberger
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  2. G. Schneider
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Corresponding author

Correspondence to G. Nürnberger .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, 37240, Tennessee, USA

    Marian Neamtu

  2. , Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, 37240, Tennessee, USA

    Larry Schumaker

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Nürnberger, G., Schneider, G. (2012). A Lagrange Interpolation Method by Trivariate Cubic C 1 Splines of Low Locality. In: Neamtu, M., Schumaker, L. (eds) Approximation Theory XIII: San Antonio 2010. Springer Proceedings in Mathematics, vol 13. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0772-0_14

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