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Basix is a finite element definition and tabulation runtime library. It is part of FEniCSx, alongside UFL, FFCx and DOLFINx (C++ docs, Python docs).
The main functionality of Basix is written in C++. Documentation of the C++ functionality of Basix can be found at docs.fenicsproject.org/basix/v0.4.0/cpp.
The majority of the functionality of Basix is available for use through the Python interface. Documentation of this interface can be found at docs.fenicsproject.org/basix/v0.4.0/python.
Installing Basix
Instructions for installing Basix can be found at docs.fenicsproject.org/basix/v0.4.0/install.html.
Source
The source code of Basix is available on GitHub. It is available under an MIT license.
Supported elements
Interval
In Basix, the sub-entities of the reference interval are numbered as follows:
The following elements are supported on an interval:
Triangle
In Basix, the sub-entities of the reference triangle are numbered as follows:
The following elements are supported on a triangle:
- Lagrange
- Nédélec first kind
- Raviart-Thomas
- Nédélec second kind
- Brezzi-Douglas-Marini
- Regge
- Hellan-Herrmann-Johnson
- Crouzeix-Raviart
- Bubble
Quadrilateral
In Basix, the sub-entities of the reference quadrilateral are numbered as follows:
The following elements are supported on a quadrilateral:
- Lagrange
- Nédélec first kind
- Raviart-Thomas
- Nédélec second kind
- Brezzi-Douglas-Marini
- Bubble
- DPC
- Serendipity
Tetrahedron
In Basix, the sub-entities of the reference tetrahedron are numbered as follows:
The following elements are supported on a tetrahedron:
- Lagrange
- Nédélec first kind
- Raviart-Thomas
- Nédélec second kind
- Brezzi-Douglas-Marini
- Regge
- Crouzeix-Raviart
- Bubble
Hexahedron
In Basix, the sub-entities of the reference hexahedron are numbered as follows:
The following elements are supported on a hexahedron:
- Lagrange
- Nédélec first kind
- Raviart-Thomas
- Nédélec second kind
- Brezzi-Douglas-Marini
- Bubble
- DPC
- Serendipity
Prism
In Basix, the sub-entities of the reference prism are numbered as follows:
The following elements are supported on a prism:
Pyramid
In Basix, the sub-entities of the reference pyramid are numbered as follows:
The following elements are supported on a pyramid: