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Reduced Hsieh–Clough–Tocher
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| Abbreviated names | rHCT, HCT-red |
| Degrees | \(k=3\) |
| Reference cells | triangle |
| DOFs | On each vertex: point evaluations, and point evaluations of first derivatives |
| Number of DOFs | triangle: \(9\) |
| Mapping | identity |
| continuity | Function values and derivatives are continuous. |
| Categories | Scalar-valued elements, Macro elements |
Implementations
This element is implemented in FIAT and Symfem .↓ Show implementation detail ↓Examples
| triangle degree 3 |  (click to view basis functions) |
References
- Clough, Ray W. and Tocher, James L. Finite element stiffness matrices for analysis of plate bending, Proceedings of the First Conference on Matrix Methods in Structural Mechanics, 515–546, 1965. [BibTeX]
- Ciarlet, Philippe G. Interpolation error estimates for the reduced Hsieh–Clough–Tocher triangle, Mathematics of Computation 32, 335–344, 1978. [DOI: 10.1090/S0025-5718-1978-0482249-1] [BibTeX]
- Kirby, Robert C. A general approach to transforming finite elements, SMAI Journal of Computational Mathematics 4, 197–224, 2018. [DOI: 10.5802/smai-jcm.33] [BibTeX]
DefElement stats
| Element added | 08 March 2021 |
| Element last updated | 04 June 2025 |