Approximation by $C^1$ Splines on Piecewise Conic Domains
Oleg Davydov, Wee Ping Yeo
TL;DR
This paper introduces a Hermite interpolation scheme for $C^1$ bivariate splines on curved domains bounded by piecewise conics, providing error bounds and advancing approximation techniques on complex geometries.
Contribution
It develops a new Hermite interpolation method with proven error bounds for $C^1$ spline spaces on piecewise conic domains, extending approximation theory to curved geometries.
Findings
Established error bounds for the interpolation scheme.
Extended $C^1$ spline approximation to curved, conic-bounded domains.
Demonstrated the scheme's effectiveness on complex geometries.
Abstract
We develop a Hermite interpolation scheme and prove error bounds for bivariate piecewise polynomial spaces of Argyris type vanishing on the boundary of curved domains enclosed by piecewise conics.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Numerical methods in engineering · Advanced Numerical Methods in Computational Mathematics