Def
Element
an encyclopedia of finite element definitions
Implemented elements
Implemented in Symfem
\(Q_{k+1,k}\times Q_{k,k+1}\)
Alfeld–Sorokina
Argyris
Arnold–Awanou H(curl)
Arnold–Awanou H(div)
Arnold–Boffi–Falk
Arnold–Winther
Bell
Bernardi–Raugel
Bernstein
Bernstein–Bézier
Bogner–Fox–Schmitt
Brezzi–Douglas–Durán–Fortin
Brezzi–Douglas–Fortin–Marini
Brezzi–Douglas–Marini
Brezzi–Douglas–Marini cubical H(curl)
Brezzi–Douglas–Marini cubical H(div)
bubble
bubble enriched Lagrange
Buffa–Christiansen
Clough–Tocher
conforming Arnold–Winther
conforming Crouzeix–Raviart
Crouzeix–Falk
Crouzeix–Raviart
direct serendipity
discontinuous polynomial cubical
discontinuous Taylor
dPc
dual polynomial
enriched Galerkin
enriched vector Galerkin
Fortin–Soulie
Gauss–Legendre
Guzmán–Neilan
Hellan–Herrmann–Johnson
Hermite
Hsieh–Clough–Tocher
Huang–Zhang
iso-P2 P1
Kong–Mulder–Veldhuizen
Lagrange
locking-free enriched Galerkin
Mardal–Tai–Winther
Morley
Morley–Wang–Xu
Nédélec (first kind)
Nédélec (second kind)
Nédélec cubical H(div)
non-conforming Crouzeix–Raviart
nonconforming Arnold–Winther
P1 macro
P1-iso-P2
P2-iso-P1
Q H(div)
Radau
Rannacher–Turek
Raviart–Thomas
Raviart–Thomas cubical H(div)
reduced Hsieh–Clough–Tocher
Regge
rotated Buffa–Christiansen
serendipity
serendipity H(curl)
serendipity H(div)
Taylor
Tiniest tensor
Tiniest tensor H(curl)
Tiniest tensor H(div)
TNT
TNT H(curl)
TNT H(div)
transition
trimmed serendipity H(curl)
trimmed serendipity H(div)
vector bubble enriched Lagrange
vector dPc
vector Lagrange
vector Q
Wu–Xu
Implemented in Basix
Brezzi–Douglas–Marini
bubble
Crouzeix–Raviart
DGT
discontinuous polynomial cubical
dPc
Galerkin
Gauss–Lobatto–Legendre
Hdiv trace
Hermite
iso-P2 P1
Lagrange
Lobatto
Nédélec
Nédélec (first kind)
Nédélec (second kind)
Nédélec cubical H(curl)
non-conforming Crouzeix–Raviart
P1-iso-P2
P2-iso-P1
Polynomial
Q
Q H(curl)
Rao–Wilton–Glisson
Raviart–Thomas
Raviart–Thomas cubical H(curl)
Regge
serendipity
Whitney
Implemented in (legacy) UFL
Argyris
Arnold–Awanou H(curl)
Arnold–Awanou H(div)
Arnold–Winther
Bell
Bernstein
Bernstein–Bézier
Brezzi–Douglas–Fortin–Marini
Brezzi–Douglas–Marini
Brezzi–Douglas–Marini cubical H(curl)
Brezzi–Douglas–Marini cubical H(div)
bubble
conforming Arnold–Winther
Crouzeix–Raviart
direct serendipity
discontinuous polynomial cubical
discontinuous Taylor
dPc
Hellan–Herrmann–Johnson
Hermite
Kong–Mulder–Veldhuizen
Lagrange
Mardal–Tai–Winther
Morley
Nédélec
Nédélec (first kind)
Nédélec (second kind)
Nédélec cubical H(div)
non-conforming Crouzeix–Raviart
nonconforming Arnold–Winther
Q H(div)
Rao–Wilton–Glisson
Raviart–Thomas
Raviart–Thomas cubical H(div)
Regge
serendipity
serendipity H(curl)
serendipity H(div)
Taylor
vector dPc
vector Lagrange
vector Q
Implemented in Bempp
Buffa–Christiansen
DGT
dual polynomial
Galerkin
Gauss–Lobatto–Legendre
Hdiv trace
Lagrange
Lobatto
Nédélec (first kind)
Nédélec cubical H(curl)
Polynomial
Q
Q H(curl)
Raviart–Thomas
Raviart–Thomas cubical H(curl)
rotated Buffa–Christiansen
Whitney
Implemented in Basix.UFL
Brezzi–Douglas–Marini
bubble
Crouzeix–Raviart
DGT
discontinuous polynomial cubical
dPc
Galerkin
Gauss–Lobatto–Legendre
Hdiv trace
iso-P2 P1
Lagrange
Lobatto
Nédélec
Nédélec (first kind)
Nédélec (second kind)
Nédélec cubical H(curl)
non-conforming Crouzeix–Raviart
P1-iso-P2
P2-iso-P1
Polynomial
Q
Q H(curl)
Rao–Wilton–Glisson
Raviart–Thomas
Raviart–Thomas cubical H(curl)
Regge
serendipity
vector dPc
vector Lagrange
vector Q
Whitney
Implemented in FIAT
Argyris
Arnold–Winther
Bernstein
Bernstein–Bézier
Brezzi–Douglas–Fortin–Marini
Brezzi–Douglas–Marini
bubble
conforming Arnold–Winther
Crouzeix–Raviart
DGT
discontinuous polynomial cubical
discontinuous Taylor
dPc
Galerkin
Gauss–Lobatto–Legendre
Hdiv trace
Hellan–Herrmann–Johnson
Hermite
Kong–Mulder–Veldhuizen
Lagrange
Lobatto
Mardal–Tai–Winther
Morley
Nédélec
Nédélec (first kind)
Nédélec (second kind)
Nédélec cubical H(curl)
non-conforming Crouzeix–Raviart
nonconforming Arnold–Winther
Polynomial
Q
Q H(curl)
Rao–Wilton–Glisson
Raviart–Thomas
Raviart–Thomas cubical H(curl)
Regge
serendipity
Taylor
trimmed serendipity H(curl)
trimmed serendipity H(div)
Whitney