Quintic Splines on Domains Enclosed by Piecewise Conics and Numerical Solution of Fully Nonlinear Elliptic Equations
arXiv:1602.05467
Abstract
We introduce bivariate 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.
19 pages