$C^1$ Quintic Splines on Domains Enclosed by Piecewise Conics and   Numerical Solution of Fully Nonlinear Elliptic Equations
  We introduce bivariate $C^1$ piecewise quintic finite element spaces for curved domains enclosed by piecewise conics satisfying homogeneous boundary conditions, construct local bases for them using Bernstein-B\'ezier techniques, and demonstrate the effectiveness of these finite elements for the numerical solution of the Monge-Amp\`ere equation over curved domains by B\"ohmer's method. 
Oleg Davydov and Abid Saeed
math.NA