print('Step:', i)
space = LagrangeFiniteElementSpace(mesh, p=p)
NDof[i] = space.number_of_global_dofs()
uh = space.function()
a = np.array([(10.0, -1.0), (-1.0, 2.0)], dtype=np.float64)
A = space.stiff_matrix(c=a)
@cartesian
def r(p):
x = p[..., 0]
y = p[..., 1]
return 1 + x**2 + y**2
M = space.mass_matrix(c=r)
b = np.array([1.0, 1.0], dtype=np.float64)
B = space.convection_matrix(c=b)
@cartesian
def f(p):
x = p[..., 0]
y = p[..., 1]
pi = np.pi
return 2 * pi**2 * np.sin(pi * x) * np.sin(
pi * y) + 12 * pi**2 * np.cos(pi * x) * np.cos(pi * y) + (
-pi) * np.sin(pi * x) * np.cos(pi * y) - pi * np.cos(
pi * x) * np.sin(pi * y) + (1 + x**2 + y**2) * np.cos(
pi * x) * np.cos(pi * y)
F = space.source_vector(f)
A += B + M
pde = CDRMODEL()
domain = pde.domain()
mf = MeshFactory()
mesh = mf.boxmesh2d(domain, nx=n, ny=n, meshtype='tri')
NDof = np.zeros(maxit, dtype=mesh.itype)
errorMatrix = np.zeros((2, maxit), dtype=mesh.ftype)
errorType = ['$|| u - u_h ||_0$', '$|| \\nabla u - \\nabla u_h||_0$']
for i in range(maxit):
print('Step:', i)
space = LagrangeFiniteElementSpace(mesh, p=p)
NDof[i] = space.number_of_global_dofs()
uh = space.function()
A = space.stiff_matrix(c=pde.diffusion_coefficient)
B = space.convection_matrix(c=pde.convection_coefficient_ndf)
M = space.mass_matrix(c=pde.reaction_coefficient)
F = space.source_vector(pde.source)
A += B
A += M
bc = DirichletBC(space, pde.dirichlet)
A, F = bc.apply(A, F, uh)
uh[:] = spsolve(A, F)
errorMatrix[0, i] = space.integralalg.error(pde.solution,
uh.value,
power=2)
errorMatrix[1, i] = space.integralalg.error(pde.gradient,
uh.grad_value,
