Approximation by $C^1$ Splines on Piecewise Conic Domains
arXiv:1612.020323 citationsh-index: 21
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Provides theoretical foundations for high-order finite element methods on curved geometries, relevant to computational mathematics and engineering simulations.
Developed a Hermite interpolation scheme for C^1 bivariate splines on curved domains bounded by piecewise conics, with proven error bounds. The method achieves optimal approximation order for smooth functions.
We develop a Hermite interpolation scheme and prove error bounds for $C^1$ bivariate piecewise polynomial spaces of Argyris type vanishing on the boundary of curved domains enclosed by piecewise conics.