hex: allow for Real function space (#3549)

firedrake/functionspaceimpl.py

@@ -50,8 +50,8 @@ def check_element(element, top=True):
         If the element is illegal.
     """
     if element.cell.cellname() == "hexahedron" and \
-       element.family() not in ["Q", "DQ"]:
-        raise NotImplementedError("Currently can only use 'Q' and/or 'DQ' elements on hexahedral meshes, not", element.family())
+       element.family() not in ["Q", "DQ", "Real"]:
+        raise NotImplementedError("Currently can only use 'Q', 'DQ', and/or 'Real' elements on hexahedral meshes, not", element.family())
     if type(element) in (finat.ufl.BrokenElement, finat.ufl.RestrictedElement,
                          finat.ufl.HDivElement, finat.ufl.HCurlElement):
         inner = (element._element, )

tests/regression/test_real_space.py

@@ -301,3 +301,17 @@ def test_real_interpolate():
     R = FunctionSpace(mesh, "R", 0)
     a_int = assemble(interpolate(Constant(1.0), R))
     assert np.allclose(float(a_int), 1.0)
+
+
+def test_real_space_hex():
+    mesh = BoxMesh(2, 1, 1, 2., 1., 1., hexahedral=True)
+    DG = FunctionSpace(mesh, "DQ", 0)
+    R = FunctionSpace(mesh, "R", 0)
+    dg = Function(DG).assign(1.)
+    r = Function(R).assign(1.)
+    val = assemble(r * dx)
+    assert abs(val - 2.) < 1.e-14
+    val = assemble(inner(dg, TestFunction(R)) * dx)
+    assert np.allclose(val.dat.data_ro, [2.])
+    val = assemble(inner(r, TestFunction(DG)) * dx)
+    assert np.allclose(val.dat.data, [1., 1.])