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Lagrange Interpolation byC1 Cubic Splines on Triangulated Quadrangulations

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Abstract

We describe local Lagrange interpolation methods based onC1 cubic splines on triangulations obtained from arbitrary strictly convex quadrangulations by adding one or two diagonals. Our construction makes use of a fast algorithm for coloring quadrangulations, and the overall algorithm has linear complexity while providing optimal order approximation of smooth functions.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Mannheim, D-618131, Mannheim, Germany

    Günther Nürnberger & Frank Zeilfelder

  2. Center for Constructive Approximation, Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA

    Larry L. Schumaker

Authors
  1. Günther Nürnberger

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  2. Larry L. Schumaker

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  3. Frank Zeilfelder

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Nürnberger, G., Schumaker, L.L. & Zeilfelder, F. Lagrange Interpolation byC1 Cubic Splines on Triangulated Quadrangulations.Advances in Computational Mathematics21, 357–380 (2004). https://doi.org/10.1023/B:ACOM.0000032044.49282.8a

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