A B-spline-like basis for the Powell-Sabin 12-split based on simplex splines

-quadratics on the well-known Powell-Sabin 12-split triangular region. Among its many important desirable properties, we show that it has an associated recurrence relation for evaluation and differentiation. Also developed are a Marsden-like identity, quasi-interpolants, approximation methods exhibi...

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Bibliographic Details
Published in:Mathematics of computation 2013-07, Vol.82 (283), p.1667-1707
Main Authors: COHEN, ELAINE, LYCHE, TOM, RIESENFELD, RICHARD F.
Format: Article
Language:English
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Summary:-quadratics on the well-known Powell-Sabin 12-split triangular region. Among its many important desirable properties, we show that it has an associated recurrence relation for evaluation and differentiation. Also developed are a Marsden-like identity, quasi-interpolants, approximation methods exhibiting unconditional stability, a subdivision scheme, and smoothness conditions across macro-element edges.]]>
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-2013-02664-6