Macro-elements and stable local bases for splines on Powell-Sabin triangulations |
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Authors: | Ming-Jun Lai Larry L Schumaker |
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Institution: | Department of Mathematics, The University of Georgia, Athens, Georgia 30602 ; Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240 |
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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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Keywords: | Macro-elements stable bases spline spaces |
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