def test_contains_h1():
h1_elements = [
# Standard Lagrange elements:
FiniteElement("CG", triangle, 1),
FiniteElement("CG", triangle, 2),
# Some special elements:
FiniteElement("AW", triangle),
FiniteElement("HER", triangle),
FiniteElement("MTW", triangle),
# Tensor product elements:
TensorProductElement(FiniteElement("CG", interval, 1),
FiniteElement("CG", interval, 1)),
TensorProductElement(FiniteElement("CG", interval, 2),
FiniteElement("CG", interval, 2)),
# Enriched elements:
EnrichedElement(FiniteElement("CG", triangle, 2),
FiniteElement("B", triangle, 3))
]
for h1_element in h1_elements:
assert h1_element in H1
assert h1_element in H1dx1dy
assert h1_element in HDiv
assert h1_element in HCurl
assert h1_element in L2
assert h1_element in H0dx0dy
assert h1_element not in H2
assert h1_element not in H2dx2dy
def test_contains_l2():
l2_elements = [
FiniteElement("Real", triangle, 0),
FiniteElement("DG", triangle, 0),
FiniteElement("DG", triangle, 1),
FiniteElement("DG", triangle, 2),
FiniteElement("CR", triangle, 1),
# Tensor product elements:
TensorProductElement(FiniteElement("DG", interval, 1),
FiniteElement("DG", interval, 1)),
TensorProductElement(FiniteElement("DG", interval, 1),
FiniteElement("CG", interval, 2)),
# Enriched element:
EnrichedElement(FiniteElement("DG", triangle, 1),
FiniteElement("B", triangle, 3))
]
for l2_element in l2_elements:
assert l2_element in L2
assert l2_element in H0dx0dy
assert l2_element not in H1
assert l2_element not in H1dx1dy
assert l2_element not in HCurl
assert l2_element not in HDiv
assert l2_element not in H2
assert l2_element not in H2dx2dy
def test_enriched_elements_hcurl():
A = FiniteElement("CG", interval, 1)
B = FiniteElement("DG", interval, 0)
AxB = TensorProductElement(A, B)
BxA = TensorProductElement(B, A)
C = FiniteElement("RTCE", quadrilateral, 1)
D = FiniteElement("DQ", quadrilateral, 0)
Q1 = TensorProductElement(C, B)
Q2 = TensorProductElement(D, A)
hcurl_elements = [
EnrichedElement(HCurl(AxB), HCurl(BxA)),
EnrichedElement(HCurl(Q1), HCurl(Q2))
]
for hcurl_element in hcurl_elements:
assert hcurl_element in HCurl
assert hcurl_element in L2
assert hcurl_element in H0dx0dy
assert hcurl_element not in H1
assert hcurl_element not in H1dx1dy
assert hcurl_element not in HDiv
assert hcurl_element not in H2
assert hcurl_element not in H2dx2dy
def reconstruct_degree(ele, N):
"""
Reconstruct an element, modifying its polynomial degree.
By default, reconstructed EnrichedElements, TensorProductElements,
and MixedElements will have the degree of the sub-elements shifted
by the same amount so that the maximum degree is N.
This is useful to coarsen spaces like NCF(N) x DQ(N-1).
:arg ele: a :class:`ufl.FiniteElement` to reconstruct,
:arg N: an integer degree.
:returns: the reconstructed element
"""
if isinstance(ele, VectorElement):
return VectorElement(PMGBase.reconstruct_degree(
ele._sub_element, N),
dim=ele.num_sub_elements())
elif isinstance(ele, TensorElement):
return TensorElement(PMGBase.reconstruct_degree(
ele._sub_element, N),
shape=ele.value_shape(),
symmetry=ele.symmetry())
elif isinstance(ele, EnrichedElement):
shift = N - PMGBase.max_degree(ele)
return EnrichedElement(
*(PMGBase.reconstruct_degree(e,
PMGBase.max_degree(e) + shift)
for e in ele._elements))
elif isinstance(ele, TensorProductElement):
shift = N - PMGBase.max_degree(ele)
return TensorProductElement(*(PMGBase.reconstruct_degree(
e,
PMGBase.max_degree(e) + shift) for e in ele.sub_elements()),
cell=ele.cell())
elif isinstance(ele, MixedElement):
shift = N - PMGBase.max_degree(ele)
return MixedElement(
*(PMGBase.reconstruct_degree(e,
PMGBase.max_degree(e) + shift)
for e in ele.sub_elements()))
else:
try:
return type(ele)(PMGBase.reconstruct_degree(ele._element, N))
except AttributeError:
return ele.reconstruct(degree=N)