Multi-sided macro-element spaces based on Clough--Tocher triangle splits with applications to hole filling

Authors:
Vera Rayevskaya;Larry L. Schumaker
Affiliations:
Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614-0506, USA;Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA
Venue:
Computer Aided Geometric Design
Year:
2005

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Abstract

C^r macro-element spaces are constructed on polygonal domains with an arbitrary number of sides. The spaces consist of polynomial supersplines defined on triangulations which have been partially refined with Clough-Tocher splits. In addition to giving dimension formulae, minimal determining sets, and nodal bases, we derive error bounds for the corresponding Hermite interpolation operators. A number of examples are presented to show how the spaces can be used to fill n-sided holes.