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| Abbreviated names | dual | 
| Degrees | \(0\leqslant k\leqslant 1\) | 
| Reference cells | dual polygon | 
| Number of DOFs | dual polygon(n): \(\begin{cases}1&k=0\\n&k=1\end{cases}\) | 
| Mapping | identity | 
| continuity | Discontinuous. (\(n=0\)) Function values are continuous. (\(n=1\))
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| Notes | These elements are defined on the barycentric dual grid. These elements are defined as a linear combination of Lagrange basis functions on the fine grid.
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| Categories | Scalar-valued elements | 
This element is implemented in 
Bempp-cl and 
Symfem .
↓ Show implementation detail ↓↑ Hide implementation detail ↑| Bempp-cl | "DUAL"↓ Show Bempp-cl examples ↓↑ Hide Bempp-cl examples ↑
 Before running this example, you must install Bempp-cl : pip3 install numba scipy meshiopip3 install bempp-cl
 This element can then be created with the following lines of Python: import bempp_cl.apigrid = bempp_cl.api.shapes.regular_sphere(1)
 
 # Create dual polynomial degree 0
 element = bempp_cl.api.function_space(grid, "DUAL", 0)
 
 # Create dual polynomial degree 1
 element = bempp_cl.api.function_space(grid, "DUAL", 1)
 
 # Create dual polynomial degree 1
 element = bempp_cl.api.function_space(grid, "DUAL", 1)
 
 # Create dual polynomial degree 1
 element = bempp_cl.api.function_space(grid, "DUAL", 1)
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| Symfem | "dual"↓ Show Symfem examples ↓↑ Hide Symfem examples ↑
 This implementation is used to compute the examples below and verify other implementations.Before running this example, you must install Symfem : pip3 install symfem This element can then be created with the following lines of Python: import symfem
 # Create dual polynomial degree 0 on a dual polygon(6)
 element = symfem.create_element("dual polygon(6)", "dual", 0)
 
 # Create dual polynomial degree 1 on a dual polygon(4)
 element = symfem.create_element("dual polygon(4)", "dual", 1)
 
 # Create dual polynomial degree 1 on a dual polygon(5)
 element = symfem.create_element("dual polygon(5)", "dual", 1)
 
 # Create dual polynomial degree 1 on a dual polygon(6)
 element = symfem.create_element("dual polygon(6)", "dual", 1)
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- Buffa, Annalisa and Christiansen, Snorre H. A dual finite element complex on the barycentric refinement, Mathematics of Computation 76, 1743–1769, 2007. [DOI: 10.1016/j.crma.2004.12.022] [BibTeX]
| Element added | 24 January 2021 | 
| Element last updated | 04 June 2025 |