A local Lagrange interpolation method based on 𝐶¹ cubic splines on Freudenthal partitions

Hecklin, Gero; Nürnberger, Günther; Schumaker, Larry; Zeilfelder, Frank

doi:10.1090/S0025-5718-07-02056-X

A local Lagrange interpolation method based on $C^{1}$ cubic splines on Freudenthal partitions
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by Gero Hecklin, Günther Nürnberger, Larry L. Schumaker and Frank Zeilfelder;

Math. Comp. 77 (2008), 1017-1036

DOI: https://doi.org/10.1090/S0025-5718-07-02056-X

Published electronically: November 20, 2007

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Abstract:

A trivariate Lagrange interpolation method based on $C^{1}$ cubic splines is described. The splines are defined over a special refinement of the Freudenthal partition of a cube partition. The interpolating splines are uniquely determined by data values, but no derivatives are needed. The interpolation method is local and stable, provides optimal order approximation, and has linear complexity.

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