$C^1$ 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 forcurved domains enclosed by piecewise conics satisfying homogeneous boundaryconditions, construct local bases for them using Bernstein-B\'ezier techniques,and demonstrate the effectiveness of these finite elements for the numericalsolution of the Monge-Amp\`ere equation over curved domains by B\"ohmer'smethod.