Abstract
Starting with a partition of a rectangular box into subboxes, it is shown how to construct a natural tetrahedral (type-4) partition and associated trivariate C 1 quintic polynomial spline spaces with a variety of useful properties, including stable local bases and full approximation power. It is also shown how the spaces can be used to solve certain Hermite and Lagrange interpolation problems.
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Schumaker, L.L., Sorokina, T. C 1 Quintic Splines on Type-4 Tetrahedral Partitions. Advances in Computational Mathematics 21, 421–444 (2004). https://doi.org/10.1023/B:ACOM.0000032045.03775.8d
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DOI: https://doi.org/10.1023/B:ACOM.0000032045.03775.8d