O. Davydov, G. Kostin and A. Saeed, Polynomial finite element method for domains enclosed by piecewise conics, CAGD, 45 (2016), 48-72. doi:10.1016/j.cagd.2015.11.002

Abstract: 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.

Preprint/postprint versions:    pdf   arXiv:1510.00849