def foo(mesh, family, degree):
V = FunctionSpace(mesh, family, 1)
u = TrialFunction(V)
v = TestFunction(V)
a = inner(grad(u), grad(v)) * dx
L = inner(f, v) * dx
bc = DirichletBC(V, Constant(0.), DomainBoundary())
u = Function(V)
solve(a == L, u, bc)
VV = VectorFunctionSpace(mesh,
family,
degree=1 if family == 'CR' else degree)
gradu = Function(VV)
for i in range(VV.num_sub_spaces()):
GRAD = weighted_gradient_matrix(mesh, i, family, degree)
gradu.vector()[VV.sub(i).dofmap().dofs()] = GRAD * u.vector()
h = mesh.hmin()
e_l2 = errornorm(u_, u, 'l2')
grade_l2 = errornorm(u_, u, 'h10')
grade_w_l2 = errornorm(gradu_, gradu, 'l2')
return h, e_l2, grade_l2, grade_w_l2
def test_WeightedGradient(V2):
expr = "+".join(["%d*x[%d]" % (i+1,i) for i in range(2)])
u = interpolate(Expression(expr, degree=3), V2)
du = Function(V2)
wx = weighted_gradient_matrix(V2.mesh(), tuple(range(2)))
for i in range(2):
du.vector()[:] = wx[i] * u.vector()
assert round(du.vector().min() - (i+1), 7) == 0
def test_WeightedGradient(V2):
expr = "+".join(["%d*x[%d]" % (i+1,i) for i in range(2)])
u = interpolate(Expression(expr, degree=3), V2)
du = Function(V2)
wx = weighted_gradient_matrix(V2.mesh(), tuple(range(2)))
for i in range(2):
du.vector()[:] = wx[i] * u.vector()
assert round(du.vector().min() - (i+1), 7) == 0
def divergence_test(mesh):
V = FunctionSpace(mesh, 'CG', 1)
W = VectorFunctionSpace(mesh, 'CG', 1)
u = interpolate(u_, W)
divu_p = project(div(u), V) # projected divergence
e_p = errornorm(divu_, divu_p, 'l2')
divu_w = Function(V)
d = mesh.geometry().dim()
u_i = Function(V)
for i in range(d):
u_i.vector()[:] = u.vector()[W.sub(i).dofmap().dofs()]
GRADi = weighted_gradient_matrix(mesh, i, 'CG', 1)
# weighted interpolated divergence
divu_w.vector()[:] += GRADi * u_i.vector()
e_w = errornorm(divu_, divu_w, 'l2')
return mesh.hmin(), e_p, e_w
def divergence_test(mesh):
V = FunctionSpace(mesh, "CG", 1)
W = VectorFunctionSpace(mesh, "CG", 1)
u = interpolate(u_, W)
divu_p = project(div(u), V) # projected divergence
e_p = errornorm(divu_, divu_p, "l2")
divu_w = Function(V)
d = mesh.geometry().dim()
u_i = Function(V)
for i in range(d):
u_i.vector()[:] = u.vector()[W.sub(i).dofmap().dofs()]
GRADi = weighted_gradient_matrix(mesh, i, "CG", 1)
# weighted interpolated divergence
divu_w.vector()[:] += GRADi * u_i.vector()
e_w = errornorm(divu_, divu_w, "l2")
return mesh.hmin(), e_p, e_w
def foo(mesh, family, degree):
V = FunctionSpace(mesh, family, 1)
u = TrialFunction(V)
v = TestFunction(V)
a = inner(grad(u), grad(v))*dx
L = inner(f, v)*dx
bc = DirichletBC(V, Constant(0.), DomainBoundary())
u = Function(V)
solve(a == L, u, bc)
VV = VectorFunctionSpace(mesh, family, degree=1 if family == 'CR' else degree)
gradu = Function(VV)
for i in range(VV.num_sub_spaces()):
GRAD = weighted_gradient_matrix(mesh, i, family, degree)
gradu.vector()[VV.sub(i).dofmap().dofs()] = GRAD*u.vector()
h = mesh.hmin()
e_l2 = errornorm(u_, u, 'l2')
grade_l2 = errornorm(u_, u, 'h10')
grade_w_l2 = errornorm(gradu_, gradu, 'l2')
return h, e_l2, grade_l2, grade_w_l2