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Abbreviated names | dual |
Degrees | \(0\leqslant k\leqslant 1\) |
Reference elements | 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. (\(n=1\)) |
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. |
Categories | Scalar-valued elements |
This element is implemented in
Bempp and
Symfem .
↓ Show implementation detail ↓↑ Hide implementation detail ↑Bempp | "DUAL" ↓ Show Bempp examples ↓↑ Hide Bempp examples ↑Before running this example, you must install Bempp: pip3 install numba scipy meshio pip3 install bempp-cl This element can then be created with the following lines of Python: import bempp.api grid = bempp.api.shapes.regular_sphere(1)
# Create dual polynomial degree 0 element = bempp.api.function_space(grid, "DUAL", 0)
# Create dual polynomial degree 1 element = bempp.api.function_space(grid, "DUAL", 1)
# Create dual polynomial degree 1 element = bempp.api.function_space(grid, "DUAL", 1)
# Create dual polynomial degree 1 element = bempp.api.function_space(grid, "DUAL", 1) |
Symfem | "dual" ↓ Show Symfem examples ↓↑ Hide Symfem examples ↑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) This implementation is used to compute the examples below and verify other implementations. |
- 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 | 16 October 2024 |