---
name: "basis"
section: "1rheolef"
platform: "linux"
package: "rheolef"
version: "7.2-4"
release: "Debian 13 (Trixie)"
platforms: ["linux"]
url: "https://new.carta.tech/basis"
---

# basis(1rheolef)

plot a finite element basis (rheolef-7.2)

## NAME

basis - plot a finite element basis (rheolef-7.2)

## SYNOPSIS

```
basis name [element] [options]
```

## DESCRIPTION

View a finite element polynomial basis on a given reference element (see **reference\_element(6)**). Alternatively, it could show the interpolation nodes.

## EXAMPLES

```
  basis P5 t
  basis P5[warburton] t
  basis P5[warburton,monomial] t
  basis 'trace(P3d)' t
  basis P3 t -node
  basis P5 t -node-side 0
  basis P5 t -node-side 1
  basis P3 T -node
  basis B7 t
  basis S7 t
  basis RT0 t
  basis RT3 t -node
  basis 'trace_n(RT5d)' t -node
  basis P3d T -node-side 1
  basis 'trace_n(RT5d)' T -node-side 1
```

## BASIS AND ELEMENT SPECIFICATIONS

The basis *name* argument is specified as for the `space` and `basis` constructor class argument (see **space(2)** and **basis(2)**). The *element* argument is one of `e`, `t`, `q`, `T`, `P`, `H` (see **reference\_element(6)**). The `gnuplot` render is used for visualization.

## THE RAW BASIS

`-raw` \
 `-fem`

 A raw basis is used for computing the Vandermonde matrix and building the Lagrange basis. The raw basis is either `monomial`, `Dubiner` or `Bernstein` while `Dubiner` is the default. This raw basis is hiden by default: it is represented by using the `-raw` option while `-fem` switch back to the default finite element basis representation. When the basis family is either `M`, for `monomial` or `D` for `Dubiner`, there is no ambiguity, and the `-raw` option could be omitted. Conversely, when the basis family is `B`, for `Bernstein`, then, there is an ambiguity and this option should be used.

Here is an example of raw basis visualization:

```
basis M4 t
basis D5 e
basis B5 e -raw
```

 Here, the `-raw` option is used to disambiguate \
\
  between the Bernstein basis as finite element basis and the Bernstein basis as a raw basis.

## REDERING OPTIONS

The `basis` command supports several modes of visualization:

- `-ndof`

   Print the basis size, i.e. the number of degrees of freedom (ndof).

- `-poly`

   Represents the polynomial functions in elevation, for 1D and 2D elements (3D elements visualization not yet supported). All basis polynomials are showed in an animation.

- `-node`

   Represents the node location, with distinct colors for each dimension associated to.

- `-node-side`

   Represents the node location, restricted on a specific side.

## OTHERS OPTIONS

`-[no]verbose`

 Print messages related to graphic files created and command system calls (this is the default).

`-[no]clean`

 Clear temporary graphic files (this is the default).

`-[no]execute`

 Execute graphic command (this is the default). The `-noexecute` variant is useful in conjunction with the `-verbose` and `-noclean` options in order to modify some render options by hand.

## LIMITATIONS

Polynomial visualization in 3D are not yet supported: future development will use paraview with volume mode and animation for scanning all basis polynomials.

## IMPLEMENTATION

This documentation has been generated from file fem/lib/basis.cc

## AUTHOR

Pierre  Saramito  \<Pierre.Saramito@imag.fr\>

## COPYRIGHT

Copyright   (C)  2000-2018  Pierre  Saramito  \<Pierre.Saramito@imag.fr\> GPLv3+: GNU GPL version 3 or later  \<http://gnu.org/licenses/gpl.html\>. This  is  free  software:  you  are free to change and redistribute it. There is NO WARRANTY, to the extent permitted by law.