Macro-elements and stable local bases for splines on Powell-Sabin triangulations

Lai, Ming-Jun; Schumaker, Larry

doi:10.1090/S0025-5718-01-01379-5

Macro-elements and stable local bases for splines on Powell-Sabin triangulations
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by Ming-Jun Lai and Larry L. Schumaker PDF

Math. Comp. 72 (2003), 335-354 Request permission

Abstract:

Macro-elements of arbitrary smoothness are constructed on Powell-Sabin triangle splits. These elements are useful for solving boundary-value problems and for interpolation of Hermite data. It is shown that they are optimal with respect to spline degree, and we believe they are also optimal with respect to the number of degrees of freedom. The construction provides local bases for certain superspline spaces defined over Powell-Sabin refinements. These bases are shown to be stable as a function of the smallest angle in the triangulation, which in turn implies that the associated spline spaces have optimal order approximation power.

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