Polynomial Finite Element Method for Domains Enclosed by Piecewise Conics
This work provides a rigorous framework for finite element methods on curved domains, which is incremental for computational mathematics.
The paper develops a polynomial finite element method for curved domains bounded by piecewise conics, constructing stable local bases, proving error bounds, and developing optimal assembly algorithms. Numerical experiments confirm effectiveness.
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.