C~1 quintic splines on domains enclosed by piecewise conics and numerical solution of fully nonlinear elliptic equations

摘要

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-Bezier techniques, and demonstrate the effectiveness of these finite elements for the numerical solution of the Monge-Ampere equation over curved domains by Boehmer's method.