Abid Saeed

Oleg Davydov, Abid Saeed

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-Ampère equation over curved domains by Böhmer's method.

Oleg Davydov, Georgii Kostin, Abid Saeed

We consider bivariate piecewise polynomial finite element spaces for curved domains bounded by piecewise conics satisfying homogeneous boundary conditions, construct stable local bases for them using Bernstein-Bézier techniques, prove error bounds and develop optimal assembly algorithms for the finite element system matrices. Numerical experiments confirm the effectiveness of the method.