an encyclopedia of finite element definitions

 Orders $$1\leqslant k$$ Reference elements interval, quadrilateral, hexahedron Polynomial set $$\mathcal{Q}_{k}$$↓ Show polynomial set definitions ↓ DOFs On each vertex: point evaluations On each edge: point evaluations at Radau points On each face: point evaluations at Radau points On each volume: point evaluations at Radau points Number of DOFs interval: $$k+1$$ (A000027)quadrilateral: $$(k+1)^2$$ (A000290)hexahedron: $$(k+1)^3$$ (A000578) Mapping identity continuity Function values are continuous. Categories Scalar-valued elements

## Implementations

 Symfem "Lagrange", variant="radau"↓ Show Symfem examples ↓ This implementation is used to compute the examples below and verify other implementations.

## Examples

 intervalorder 1 (click to view basis functions) intervalorder 2 (click to view basis functions) quadrilateralorder 1 (click to view basis functions) quadrilateralorder 2 (click to view basis functions)

## DefElement stats

 Element added 20 February 2021 Element last updated 16 September 2023