Vector Lagrange
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Orders | \(0\leqslant k\) |
Reference elements | triangle, tetrahedron |
Polynomial set | \(\mathcal{P}_{k}^d\) ↓ Show polynomial set definitions ↓↑ Hide polynomial set definitions ↑\(\mathcal{P}_k=\operatorname{span}\left\{\prod_{i=1}^dx_i^{p_i}\middle|\sum_{i=1}^dp_i\leqslant k\right\}\) |
DOFs | On each vertex: point evaluations in coordinate directions
On each edge: point evaluations in coordinate directions
On each face: point evaluations in coordinate directions
On each volume: point evaluations in coordinate directions |
Number of DOFs | triangle: \((k+1)(k+2)\) (A002378) tetrahedron: \((k+1)(k+2)(k+3)/2\) (A027480) |
Mapping | identity |
continuity | Function values are continuous. |
Categories | Vector-valued elements |
Implementations
Symfem | "vector Lagrange" ↓ 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 vector Lagrange order 1 on a triangle element = symfem.create_element("triangle", "vector Lagrange", 1)
# Create vector Lagrange order 2 on a triangle element = symfem.create_element("triangle", "vector Lagrange", 2)
# Create vector Lagrange order 1 on a tetrahedron element = symfem.create_element("tetrahedron", "vector Lagrange", 1)
# Create vector Lagrange order 2 on a tetrahedron element = symfem.create_element("tetrahedron", "vector Lagrange", 2) |
UFL | "Lagrange" ↓ Show UFL examples ↓↑ Hide UFL examples ↑Before trying this example, you must install UFL: pip3 install UFL This element can then be created with the following lines of Python: import ufl
# Create vector Lagrange order 1 on a triangle element = ufl.VectorElement("Lagrange", "triangle", 1)
# Create vector Lagrange order 2 on a triangle element = ufl.VectorElement("Lagrange", "triangle", 2)
# Create vector Lagrange order 1 on a tetrahedron element = ufl.VectorElement("Lagrange", "tetrahedron", 1)
# Create vector Lagrange order 2 on a tetrahedron element = ufl.VectorElement("Lagrange", "tetrahedron", 2) |
Examples
DefElement stats
Element added | 30 December 2020 |
Element last updated | 02 August 2022 |