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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Smooth macro-elements on Powell-Sabin-12 splits


Authors: Larry L. Schumaker and Tatyana Sorokina
Journal: Math. Comp. 75 (2006), 711-726
MSC (2000): Primary 41A15, 65M60, 65N30
Published electronically: December 30, 2005
MathSciNet review: 2196988
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Abstract: Macro-elements of smoothness $ C^r$ are constructed on Powell- Sabin-$ 12$ splits of a triangle for all $ r \ge 0$. These new elements complement those recently constructed on Powell-Sabin-$ 6$ splits and can be used to construct convenient superspline spaces with stable local bases and full approximation power that can be applied to the solution of boundary-value problems and for interpolation of Hermite data.


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Additional Information

Larry L. Schumaker
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
Email: s@mars.cas.vanderbilt.edu

Tatyana Sorokina
Affiliation: Department of Mathematics, The University of Georgia, Athens, Georgia 30602

DOI: http://dx.doi.org/10.1090/S0025-5718-05-01813-2
PII: S 0025-5718(05)01813-2
Keywords: Macro-elements, stable bases, spline spaces, Powell-Sabin
Received by editor(s): October 29, 2004
Received by editor(s) in revised form: February 14, 2005
Published electronically: December 30, 2005
Additional Notes: The first author was supported by the Army Research Office under grant DAAD-19-99-1-0160
Article copyright: © Copyright 2005 American Mathematical Society