O. Davydov and A. Saeed, C1 quintic splines on domains enclosed by piecewise conics and numerical solution of fully nonlinear elliptic equations, Applied Numerical Mathematics, 116 (2017), 172-183. doi:10.1016/j.apnum.2016.10.002

Abstract: 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-Bézier techniques, and demonstrate the effectiveness of these finite elements for the numerical solution of the Monge-Amp\`ere equation over curved domains by Böhmer's method.

Preprint/postprint versions:    pdf   arXiv:1602.05467