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# Finite Element Spaces

The definition

    define fespace <name> <flaglist>

defines the finite element space `<name>`. Example:

    define fespace v -order=2 -dim=3

There are various classes of finite element spaces. Default are continuous, nodal-valued finite element spaces. The following define flags select the type of spaces

> non of the flags below | continuous nodal finite element space
> `-hcurl` | H(curl) finite elements (Nedelec-type, edge elements)
> `-hdiv` | H(div) finite elements (Raviart-Thomas, face elements)
> `-l2` | non-continuous elements, element by element
> `-l2surf` | element by element on surface
> `-h1ho` | Arbitrary order continuous elements
> `-hcurlho` | Arbitrary order H(curl) elements
> `-hdivho` | Arbitrary order H(div) elements
> `-l2ho` | Arbitrary order non-continuous elements

The following flags specify the finite element spaces

> `-order=<num>` | Order of finite elements
> `-dim=<num>` | Number of fields (number of copies of fe), 2 for 2D elasticity
> `-vec` | set -dim=spacedim
> `-tensor` | set -dim=spacedim*spacedim
> `-symtensor` | set -dim=spacedim * (spacedim+1) / 2, (symmetric stress tensor)
> `-complex` | complex valued fe-space

A compound fe-space combines several fe-spaces to a new one. Useful, e.g., for Reissner-Mindlin plate models containing the deflection w and two rotations beta:

    fespace vw -order=2
    fespace vbeta -order=1
    fespace v -compound -spaces=[vw,vbeta,vbeta]

The fespace maintains the degrees of freedom. On mesh refinement, the space provides the grid transfer operator (prolongation). High order fe spaces maintain a lowest-order fespace of the same type for preconditioning.

Subsections

- H1-Finite Element Space

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