Stable Splitting of Bivariate Splines Spaces by Bernstein-Bézier Methods

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.