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P1-iso-P2

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Alternative names	P2-iso-P1, iso-P2 P1
Orders	\(k=1\)
Reference elements	interval, triangle, quadrilateral
DOFs	On each vertex: point evaluations On each edge: point evaluations On each face: point evaluations
Number of DOFs	interval: \(3\) triangle: \(6\) quadrilateral: \(9\)
Number of DOFs on subentities	vertices: \(1\) edges: \(1\) faces: \(0\) (triangle), \(1\) (quadrilateral)
Mapping	identity
continuity	Function values are continuous.
Categories	Scalar-valued elements, Macro elements

Implementations

Basix	`basix.ElementFamily.iso` ↓ Show Basix examples ↓↑ Hide Basix examples ↑ Before trying this example, you must install Basix: pip3 install git+https://github.com/FEniCS/basix.git This element can then be created with the following lines of Python: import basix # Create P1-iso-P2 order 1 on a interval element = basix.create_element(basix.ElementFamily.iso, basix.CellType.interval, 1) # Create P1-iso-P2 order 1 on a triangle element = basix.create_element(basix.ElementFamily.iso, basix.CellType.triangle, 1) # Create P1-iso-P2 order 1 on a quadrilateral element = basix.create_element(basix.ElementFamily.iso, basix.CellType.quadrilateral, 1) This implementation is correct for all the examples below.
Basix.UFL	`basix.ElementFamily.iso` ↓ Show Basix.UFL examples ↓↑ Hide Basix.UFL examples ↑ Before trying this example, you must install Basix.UFL: pip3 install git+https://github.com/FEniCS/basix.git git+https://github.com/FEniCS/ufl.git This element can then be created with the following lines of Python: import basix import basix.ufl # Create P1-iso-P2 order 1 on a interval element = basix.ufl.element(basix.ElementFamily.iso, basix.CellType.interval, 1) # Create P1-iso-P2 order 1 on a triangle element = basix.ufl.element(basix.ElementFamily.iso, basix.CellType.triangle, 1) # Create P1-iso-P2 order 1 on a quadrilateral element = basix.ufl.element(basix.ElementFamily.iso, basix.CellType.quadrilateral, 1) This implementation is correct for all the examples below.
Symfem	`"P1-iso-P2"` ↓ Show Symfem examples ↓↑ Hide Symfem examples ↑ Before trying this example, you must install Symfem: pip3 install symfem This element can then be created with the following lines of Python: import symfem # Create P1-iso-P2 order 1 on a interval element = symfem.create_element("interval", "P1-iso-P2", 1) # Create P1-iso-P2 order 1 on a triangle element = symfem.create_element("triangle", "P1-iso-P2", 1) # Create P1-iso-P2 order 1 on a quadrilateral element = symfem.create_element("quadrilateral", "P1-iso-P2", 1) This implementation is used to compute the examples below and verify other implementations.

Examples

interval order 1	(click to view basis functions)
triangle order 1	(click to view basis functions)
quadrilateral order 1	(click to view basis functions)

References

Bercovier, Michel and Pironneau, Olivier. Error estimates for finite element method solution of the Stokes problem in the primitive variables, Numerische Mathematik 33, 211–224, 1979. [DOI: 10.1007/BF01399555] [BibTeX]

DefElement stats

Element added	06 July 2022
Element last updated	16 September 2023