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Morley
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| Degrees | \(k=2\) where \(k\) is the polynomial subdegree |
| Polynomial subdegree | \(k\) |
| Polynomial superdegree | \(k\) |
| Reference cells | triangle |
| Finite dimensional space | \(\mathcal{P}_{k}\) ↓ Show set definitions ↓ |
| DOFs | On each vertex: point evaluations On each edge: point evaluations of normal derivatives at midpoints |
| Number of DOFs | triangle: \(6\) |
| Mapping | see [2] |
| continuity | Function values are continuous. |
| Notes | The normal derivatives of the basis functions are continuous between cells |
| Categories | Scalar-valued elements |
Implementations
This element is implemented in FIAT and Symfem .↓ Show implementation detail ↓Examples
| triangle degree 2 |  (click to view basis functions) |
References
- [1] Morley, L. S. D. The triangular equilibrium element in the solution of plate bending problems, The Aeronautical Quarterly 19(2), 149–169, 1968. [DOI: 10.1017/S0001925900004546] [BibTeX]
- [2] Kirby, Robert C. A general approach to transforming finite elements, The SMAI journal of computational mathematics 4, 197–224, 2018. [DOI: 10.5802/smai-jcm.33] [BibTeX]
DefElement stats
| Element added | 09 January 2021 |
| Element last updated | 20 November 2025 |