C1 quintic splines on domains enclosed by piecewise conics and numerical solution of fully nonlinear elliptic equations

We introduce bivariate C1 piecewise quintic finite element spaces for curved domains enclosed by piecewise conics satisfying homogeneous boundary conditions, construct local bases for them using Bernstein-Bézier techniques, and demonstrate the effectiveness of these finite elements for the numerical solution of the Monge-Ampère equation over curved domains by Böhmer's method.