an encyclopedia of finite element definitions

Taylor

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Alternative namesdiscontinuous Taylor
Orders\(0\leqslant k\)
Reference elementsinterval, triangle, tetrahedron
Polynomial set\(\mathcal{P}_{k}\)
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DOFsOn the interior of the reference element: integral over cell, and point evaluations at midpoint of derivatives up to order \(k\)
Number of DOFsinterval: \(k+1\) (A000027)
triangle: \((k+1)(k+2)/2\) (A000217)
tetrahedron: \((k+1)(k+2)(k+3)/6\) (A000292)
Mappingidentity
continuityFunction values are continuous.
CategoriesScalar-valued elements

Implementations

Symfem"Taylor"
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UFL"TDG"
↓ Show UFL examples ↓

Examples

interval
order 1
(click to view basis functions)
interval
order 2
(click to view basis functions)
interval
order 3
(click to view basis functions)
triangle
order 1
(click to view basis functions)
triangle
order 2
(click to view basis functions)
triangle
order 3
(click to view basis functions)

DefElement stats

Element added01 March 2021
Element last updated02 August 2022