arXiv subjects

Abid Saeed

Publications and source records attributed to Abid Saeed.

2 recordsLinked to original sources

arXiv2016

$C^1$ Quintic Splines on Domains Enclosed by Piecewise Conics and Numerical Solution of Fully Nonlinear Elliptic Equations

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-B\'ezier techniques, and demonstrate the effectiveness of these finite elements for the numerical solution of the Monge-Amp\`ere equation over curved domains by B\"ohmer's method.

math.NA↗

arXiv2015

Polynomial Finite Element Method for Domains Enclosed by Piecewise Conics

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-B\'ezier techniques, prove error bounds and develop optimal assembly algorithms for the finite element system matrices. Numerical experiments confirm the effectiveness of the method.

math.NA↗