FunctionSpace

class dolfin.functions.functionspace.FunctionSpace(*args, **kwargs)

Bases: ufl.functionspace.FunctionSpace, dolfin.cpp.function.FunctionSpace

Base class for all function spaces.

Create finite element function space.

Overloaded versions

• FunctionSpace(mesh, element, constrained_domain=None)

  Create function space on given mesh for given finite element

• FunctionSpace(mesh, family, degree, form_degree=None,

  constrained_domain=None, restriction=None)

  Convenience function for specifying element by string, degree, etc.

• FunctionSpace(cppV)

  Internal library function for wrapping :py:class`cpp.FunctionSpace <dolfin.cpp.FunctionSpace>` into FunctionSpace. No copying is done.

Arguments

mesh (Mesh)

the mesh

element (ufl.FiniteElement)

the element

family (string)

specification of the element family, see below for alternatives.

degree (int)

the degree of the element.

form_degree (int)

the form degree (FEEC notation, used when field is viewed as k-form)

constrained_domain

constrained subdomain with map function.

restriction

restriction of the element (e.g. to cell facets).

Which families and degrees that are supported is determined by the form compiler used to generate the element, but typical families include

Name	Usage
Argyris*	“ARG”
Arnold-Winther*	“AW”
Brezzi-Douglas-Fortin-Marini*	“BDFM”
Brezzi-Douglas-Marini	“BDM”
Bubble	“B”
Crouzeix-Raviart	“CR”
Discontinuous Lagrange	“DG”
Discontinuous Raviart-Thomas	“DRT”
Hermite*	“HER”
Lagrange	“CG”
Mardal-Tai-Winther*	“MTW”
Morley*	“MOR”
Nedelec 1st kind H(curl)	“N1curl”
Nedelec 2nd kind H(curl)	“N2curl”
Quadrature	“Quadrature”
Raviart-Thomas	“RT”
Real	“R”

*only partly supported.

Examples of usage

To define a discrete function space over e.g. the unit square:

mesh = UnitSquare(32,32)
V = FunctionSpace(mesh, "CG", 1)

Here, "CG" stands for Continuous Galerkin, implying the standard Lagrange family of elements. Instead of "CG", we could have written "Lagrange". With degree 1, we get the linear Lagrange element. Other examples include:

# Discontinuous element of degree 0
V = FunctionSpace(mesh, "DG", 0)

# Brezzi-Douglas-Marini element of degree 2
W = FunctionSpace(mesh, "BDM", 2)

# Real element with one global degree of freedom
R = FunctionSpace(mesh, "R", 0)

cell()

Return the UFL cell.

collapse(collapsed_dofs=False)

Collapse a subspace and return a new function space and a map from new to old dofs

Arguments

collapsed_dofs (bool)

Return the map from new to old dofs

Returns

_FunctionSpace_

The new function space.

dict

The map from new to old dofs (optional)

dolfin_element()

Return the DOLFIN element.

extract_sub_space(component)

Extract subspace for component

Arguments

component (numpy.array(uint))

The component.

Returns

_FunctionSpace_

The subspace.

num_sub_spaces()

Return the number of sub spaces

split()

Split a mixed functionspace into its sub spaces

sub(i)

Return the i-th sub space

ufl_cell()

Return the UFL cell.

ufl_function_space()