an encyclopedia of finite element definitions

# Taylor

 Alternative names discontinuous Taylor Orders $$0\leqslant k$$ Reference elements interval, triangle, tetrahedron Polynomial set $$\mathcal{P}_{k}$$↓ Show polynomial set definitions ↓ DOFs On the interior of the reference element: integral over cell, and point evaluations at midpoint of derivatives up to order $$k$$ Number of DOFs interval: $$k+1$$ (A000027)triangle: $$(k+1)(k+2)/2$$ (A000217)tetrahedron: $$(k+1)(k+2)(k+3)/6$$ (A000292) Mapping identity continuity Function values are continuous. Categories Scalar-valued elements

## Implementations

 FIAT FIAT.DiscontinuousTaylor↓ Show FIAT examples ↓ This implementation is correct for all the examples below. Symfem "Taylor"↓ Show Symfem examples ↓ This implementation is used to compute the examples below and verify other implementations. (legacy) UFL "TDG"↓ Show (legacy) UFL examples ↓

## Examples

 intervalorder 1 (click to view basis functions) intervalorder 2 (click to view basis functions) intervalorder 3 (click to view basis functions) triangleorder 1 (click to view basis functions) triangleorder 2 (click to view basis functions) triangleorder 3 (click to view basis functions)

## DefElement stats

 Element added 01 March 2021 Element last updated 16 September 2023