$C^1$ Quintic Splines on Domains Enclosed by Piecewise Conics and Numerical Solution of Fully Nonlinear Elliptic Equations
Numerical Analysis
2025-08-26 v1
Abstract
We introduce bivariate 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.
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Cite
@article{arxiv.1602.05467,
title = {$C^1$ Quintic Splines on Domains Enclosed by Piecewise Conics and Numerical Solution of Fully Nonlinear Elliptic Equations},
author = {Oleg Davydov and Abid Saeed},
journal= {arXiv preprint arXiv:1602.05467},
year = {2025}
}
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19 pages