Stable splitting of bivariate spline spaces by Bernstein-Bézier methods

Davydov, Oleg and Saeed, Abid; Boissonnat et al, J.D., ed. (2012) Stable splitting of bivariate spline spaces by Bernstein-Bézier methods. In: Curves and Surfaces. Lecture Notes in Computer Science, 6920 . Springer-Verlag, FRA, pp. 220-235. ISBN 978-3-642-27412-1

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    Abstract

    We develop stable splitting of the minimal determining sets for the spaces of bivariate C1 splines on triangulations, including a modified Argyris space, Clough-Tocher, Powell-Sabin and quadrilateral macro-element spaces. This leads to the stable splitting of the corresponding bases as required in Böhmer's method for solving fully nonlinear elliptic PDEs on polygonal domains.