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A local Lagrange interpolation method based on $ C^{1}$ cubic splines on Freudenthal partitions

Author(s): Gero Hecklin; Günther Nürnberger; Larry L. Schumaker; Frank Zeilfelder.
Journal: Math. Comp. 77 (2008), 1017-1036.
MSC (2000): Primary 41A15, 41A05, 65D05, 65D07, 65D17, 41A63
Posted: 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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Additional Information:

Gero Hecklin
Affiliation: Institute for Mathematics, University of Mannheim, 68131 Mannheim, Germany
Email: hecklin@web.de

Günther Nürnberger
Affiliation: Institute for Mathematics, University of Mannheim, 68131 Mannheim, Germany
Email: nuern@rumms.uni-mannheim.de

Larry L. Schumaker
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
Email: larry.schumaker@vanderbilt.edu

Frank Zeilfelder
Affiliation: Institute for Mathematics, University of Mannheim, 68131 Mannheim, Germany
Email: zeilfeld@math.uni-mannheim.de

DOI: 10.1090/S0025-5718-07-02056-X
PII: S 0025-5718(07)02056-X
Keywords: Trivariate splines, local Lagrange interpolation, Freudenthal partitions
Received by editor(s): August 17, 2006
Received by editor(s) in revised form: February 16, 2007
Posted: November 20, 2007
Copyright of article: Copyright 2007, American Mathematical Society

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