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

-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

The following flags specify the finite element spaces

-order=<num>	Order of finite elements (1..linear) nodal and element of arbitrary order, hcurl and hdiv up to order 2
-hb	use hierarchical basis, (otherwise nodal)
-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, (3 for 2D elasticity, 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.