Function functionspace

python/dolfinx/fem/function.py:645–708

Create a finite element function space. Args: mesh: Mesh that space is defined on. element: Finite element description. Returns: A function space.

(
    mesh: Mesh,
    element: (
        ufl.finiteelement.AbstractFiniteElement
        | ElementMetaData
        | tuple[str, int]
        | tuple[str, int, tuple]
        | tuple[str, int, tuple, bool]
    ),
)

def functionspace(
    mesh: Mesh,
    element: (
        ufl.finiteelement.AbstractFiniteElement
        | ElementMetaData
        | tuple[str, int]
        | tuple[str, int, tuple]
        | tuple[str, int, tuple, bool]
    ),
) -> FunctionSpace:
    """Create a finite element function space.

    Args:
        mesh: Mesh that space is defined on.
        element: Finite element description.

    Returns:
        A function space.
    """
    # Create UFL element
    dtype = mesh.geometry.x.dtype
    try:
        e = ElementMetaData(*element)  # type: ignore
        ufl_e = basix.ufl.element(
            e.family,
            mesh.basix_cell(),  # type: ignore
            e.degree,
            shape=e.shape,
            symmetry=e.symmetry,
            dtype=dtype,
        )
    except TypeError:
        ufl_e = element  # type: ignore

    # Check that element and mesh cell types match
    if ((domain := mesh.ufl_domain()) is None) or ufl_e.cell != domain.ufl_cell():
        raise ValueError("Non-matching UFL cell and mesh cell shapes.")
    # Create DOLFINx objects
    element = finiteelement(mesh.topology.cell_type, ufl_e, dtype)  # type: ignore

    if ufl_e.is_real:
        cpp_dofmap = _cpp.fem.build_real_element_dofmap(
            mesh.topology._cpp_object,
            element.basix_element.entity_dofs,  # type: ignore
            element.basix_element.entity_closure_dofs,  # type: ignore
            int(np.prod(element.value_shape)),  # type: ignore
        )
    else:
        cpp_dofmap = _cpp.fem.create_dofmap(
            mesh.comm,
            mesh.topology._cpp_object,
            element._cpp_object,  # type: ignore
        )
    assert np.issubdtype(mesh.geometry.x.dtype, element.dtype), (  # type: ignore
        "Mesh and element dtype are not compatible."
    )

    # Initialize the cpp.FunctionSpace