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Gauss–Lobatto–Legendre

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Abbreviated namesGLL
Orders\(1\leqslant k\)
Reference elementsinterval, quadrilateral, hexahedron
Polynomial set\(\mathcal{Q}_{k}\)
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DOFsOn each vertex: point evaluations
On each edge: point evaluations at GLL points
On each face: point evaluations at GLL points
On each volume: point evaluations at GLL points
Number of DOFsinterval: \(k+1\) (A000027)
quadrilateral: \((k+1)^2\) (A000290)
hexahedron: \((k+1)^3\) (A000578)
Mappingidentity
continuityFunction values are continuous.
CategoriesScalar-valued elements

Implementations

Basixbasix.ElementFamily.P, ..., basix.LagrangeVariant.gll_warped
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Symfem"Lagrange", variant="lobatto"
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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)
interval
order 4
(click to view basis functions)
quadrilateral
order 1
(click to view basis functions)
quadrilateral
order 2
(click to view basis functions)

DefElement stats

Element added10 February 2021
Element last updated02 August 2022