def test_poisson_equation(self, p=1, maxit=4):
h = 0.1
pde = CosCosData()
domain = pde.domain()
error = np.zeros((maxit,), dtype=np.float)
for i in range(maxit):
mesh = triangle(domain, h, meshtype='polygon')
dmodel = SobolevEquationWGModel2d(self.pde, mesh, p=p)
uh = dmodel.space.function()
dmodel.space.set_dirichlet_bc(uh, pde.dirichlet)
S = dmodel.space.stabilizer_matrix()
A = dmodel.G + S
F = dmodel.space.source_vector(pde.source)
F -= A@uh
isBdDof = dmodel.space.boundary_dof()
gdof = dmodel.space.number_of_global_dofs()
bdIdx = np.zeros(gdof, dtype=np.int)
bdIdx[isBdDof] = 1
Tbd = spdiags(bdIdx, 0, gdof, gdof)
T = spdiags(1-bdIdx, 0, gdof, gdof)
A = T@A@T + Tbd
F[isBdDof] = uh[isBdDof]
uh[:] = spsolve(A, F)
integralalg = dmodel.space.integralalg
error[i] = integralalg.L2_error(pde.solution, uh)
h /= 2
print(error)
print(error[0:-1]/error[1:])
def test_poisson_fem_2d():
degree = 1
dim = 2
nrefine = 4
maxit = 4
from fealpy.pde.poisson_2d import CosCosData as PDE
pde = PDE()
mesh = pde.init_mesh(n=nrefine)
errorMatrix = np.zeros((2, maxit), dtype=np.float64)
NDof = np.zeros(maxit, dtype=np.int64)
for i in range(maxit):
space = LagrangeFiniteElementSpace(mesh, p=degree)
NDof[i] = space.number_of_global_dofs()
bc = DirichletBC(space, pde.dirichlet)
uh = space.function()
A = space.stiff_matrix()
F = space.source_vector(pde.source)
A, F = bc.apply(A, F, uh)
uh[:] = spsolve(A, F).reshape(-1)
errorMatrix[0, i] = space.integralalg.L2_error(pde.solution, uh)
errorMatrix[1, i] = space.integralalg.L2_error(pde.gradient, uh.grad_value)
if i < maxit-1:
mesh.uniform_refine()
def poisson_fem_2d_neuman_test(self, p=1):
pde = CosCosData()
mesh = pde.init_mesh(n=2)
for i in range(4):
space = LagrangeFiniteElementSpace(mesh, p=p)
A = space.stiff_matrix()
b = space.source_vector(pde.source)
uh = space.function()
bc = BoundaryCondition(space, neuman=pde.neuman)
bc.apply_neuman_bc(b)
c = space.integral_basis()
AD = bmat([[A, c.reshape(-1, 1)], [c, None]], format='csr')
bb = np.r_[b, 0]
x = spsolve(AD, bb)
uh[:] = x[:-1]
area = np.sum(space.integralalg.cellmeasure)
ubar = space.integralalg.integral(pde.solution,
barycenter=False) / area
def solution(p):
return pde.solution(p) - ubar
error = space.integralalg.L2_error(solution, uh)
print(error)
mesh.uniform_refine()
def test_polation_interoperator(self):
pde = CosCosData()
maxit = 4
errorType = ['$|u_I - u_h|_{max}$']
Maxerror = np.zeros((len(errorType), maxit), dtype=np.float)
NE = np.zeros(maxit, )
for i in range(maxit):
start3 = time.time()
mesh = self.mesh
isBDEdge = mesh.ds.boundary_edge_flag()
NE[i] = mesh.number_of_edges()
h = mesh.hx
bc = mesh.entity_barycenter('cell')
ec = mesh.entity_barycenter('edge')
uI = mesh.polation_interoperator(pde.solution(bc))
uh = pde.solution(ec)
Maxerror[0, i] = np.sqrt(np.sum(h**2 * (uh - uI)**2))
# Maxerror[0, i] = max(abs(uh - uI))
end3 = time.time()
print('time of %d iteration' % i, end3 - start3)
if i < maxit - 1:
mesh.uniform_refine()
showmultirate(plt, 0, NE, Maxerror, errorType)
print('Maxerror', Maxerror)
plt.show()
def interpolation(self, n=0, p=0, plot=True):
box = [-0.5, 1.5, -0.5, 1.5]
pde = CosCosData()
mesh = pde.init_mesh(n=n, meshtype='tri')
space = RaviartThomasFiniteElementSpace2d(mesh, p=p)
uI = space.interpolation(pde.flux)
error = space.integralalg.L2_error(pde.flux, uI)
print(error)
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes, box=box)
plt.show()
def poisson_fem_2d_test(self, p=1):
pde = CosCosData()
mesh = pde.init_mesh(n=3)
for i in range(4):
space = LagrangeFiniteElementSpace(mesh, p=p)
A = space.stiff_matrix()
b = space.source_vector(pde.source)
uh = space.function()
bc = BoundaryCondition(space, dirichlet=pde.dirichlet)
A, b = bc.apply_dirichlet_bc(A, b, uh)
uh[:] = spsolve(A, b).reshape(-1)
error = space.integralalg.L2_error(pde.solution, uh)
print(error)
mesh.uniform_refine()
def test_cbar(self):
dt = 0
start4 = time.time()
mesh = self.mesh
pde = CosCosData()
bc = mesh.entity_barycenter('cell')
ch = pde.solution(bc)
NC = mesh.number_of_cells()
cellidx = np.arange(NC)
xbar = bc - dt
cbar = mesh.cbar_interpolation(ch, cellidx, xbar)
end4 = time.time()
print('test_cbar time', end4 - start4)
print('cbar', sum(cbar - ch))
def plane_pmesh():
pde = CosCosData()
mesh = pde.init_mesh(n=0)
node = mesh.entity('node')
cell = mesh.entity('cell')
NN = mesh.number_of_nodes()
pnode = np.zeros((2 * NN, 3), dtype=mesh.ftype)
pnode[:NN, 0:2] = node
pnode[NN:, 0:2] = node
pnode[NN:, 2] = 1
pcell = np.r_['1', cell, cell + NN]
pmesh = PrismMesh(pnode, pcell)
return pmesh
def interpolation(self, n=0, p=0):
pde = CosCosData()
mesh = pde.init_mesh(n=n, meshtype='tri')
space = RaviartThomasFiniteElementSpace2d(mesh, p=p)
uI = space.interpolation(pde.flux)
print(space.basis.coordtype)
u = Function(space)
u[:] = uI
qf = mesh.integrator(3, 'cell')
bcs, ws = qf.get_quadrature_points_and_weights()
error = space.integralalg.L2_error(pde.source, u.div_value)
print('error:', error)
print(dir(u))
def project_test(self, p=2, m=0):
if m == 0:
node = np.array([(0.0, 0.0), (1.0, 0.0), (1.0, 1.0), (0.0, 1.0)],
dtype=np.float)
cell = np.array([0, 1, 2, 3], dtype=np.int)
cellLocation = np.array([0, 4], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
elif m == 1:
pde = CosCosData()
qtree = pde.init_mesh(n=4, meshtype='quadtree')
mesh = qtree.to_polygonmesh()
points = np.array([[(0.5, 0.5), (0.6, 0.6)]], dtype=np.float)
space = ScaledMonomialSpace2d(mesh, p)
gphi = space.grad_basis(points)
print(gphi)
def test_space_on_triangle(self, p=3):
pde = CosCosData()
mesh = pde.init_mesh(0)
space = LagrangeFiniteElementSpace(mesh, p=p)
ips = space.interpolation_points()
face2dof = space.dof.face_to_dof()
print(face2dof)
print(mesh.entity('cell'))
print('cell2dof:', space.cell_to_dof())
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, node=ips, showindex=True)
mesh.find_edge(axes, showindex=True)
plt.show()
def sympy_compute(self, plot=True):
import sympy as sp
from sympy.abc import x, y, z
if plot:
pde = CosCosData()
mesh = pde.init_mesh(n=0, meshtype='tri')
n = mesh.edge_unit_normal()
print("n:\n", n)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_edge(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
def print_method(self, n=0, p=0):
pde = CosCosData()
mesh = pde.init_mesh(n=n, meshtype='tri')
space = LagrangeFiniteElementSpace(mesh, p=p)
array = space.array(dim=2)
uI = Function(space, array=array)
qf = mesh.integrator(3, 'cell')
bcs, ws = qf.get_quadrature_points_and_weights()
print("__call__:", uI(bcs))
print("value:", uI.value(bcs))
print(uI[1:2])
print(uI.index(0))
print(uI.__dict__)
def interpolation(self, n=2, plot=True):
from fealpy.pde.poisson_2d import CosCosData
from fealpy.functionspace import ConformingVirtualElementSpace2d
pde = CosCosData()
node = np.array([(0, 0), (1, 0), (1, 1), (0, 1)], dtype=np.float64)
cell = np.array([(0, 1, 2, 3)], dtype=np.int_)
mesh = QuadrangleMesh(node, cell)
#mesh = PolygonMesh.from_mesh(mesh)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.uniform_refine(n=n)
#mesh.print()
space = ConformingVirtualElementSpace2d(mesh, p=1)
uI = space.interpolation(pde.solution)
up = space.project_to_smspace(uI)
error = space.integralalg.L2_error(pde.solution, up)
print(error)
if plot:
fig = plt.figure()
axes = fig.gca()
#mesh.add_halfedge_plot(axes, showindex=True)
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_edge(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
def test_poisson():
p = 1 # 有限元空间次数, 可以增大 p， 看输出结果的变化
n = 4 # 初始网格加密次数
maxit = 4 # 最大迭代次数
pde = PDE()
mesh = pde.init_mesh(n=n)
errorMatrix = np.zeros((2, maxit), dtype=np.float)
NDof = np.zeros(maxit, dtype=np.float)
for i in range(maxit):
space = LagrangeFiniteElementSpace(mesh, p=p) # 建立有限元空间
NDof[i] = space.number_of_global_dofs() # 有限元空间自由度的个数
bc = DirichletBC(space, pde.dirichlet) # DirichletBC 条件
uh = space.function() # 有限元函数
A = space.stiff_matrix() # 刚度矩阵
F = space.source_vector(pde.source) # 载荷向量
A, F = bc.apply(A, F, uh) # 处理边界条件
uh[:] = spsolve(A, F).reshape(-1) # 稀疏矩阵直接解法器
# ml = pyamg.ruge_stuben_solver(A) # 代数多重网格解法器
# uh[:] = ml.solve(F, tol=1e-12, accel='cg').reshape(-1)
errorMatrix[0, i] = space.integralalg.L2_error(
pde.solution, uh
) # 计算 L2 误差
errorMatrix[1, i] = space.integralalg.L2_error(
pde.gradient, uh.grad_value
) # 计算 H1 误差
if i < maxit - 1:
mesh.uniform_refine() # 一致加密网格
assert (errorMatrix < 1.0).all()
class QuadBilinearFiniteElementSpaceTest:
def __init__(self):
self.pde = CosCosData()
self.mesh = self.pde.init_mesh(meshtype='quad')
self.space = QuadBilinearFiniteElementSpace(self.mesh)
def test_intetpolation(self):
pass
def test_projection(self):
pass
def test_sovle_poisson_equation(self):
pass
def test_interpolation(self):
start2 = time.time()
pde = CosCosData()
F0 = self.mesh.interpolation(pde.solution, intertype='node')
print(F0.shape)
F1 = self.mesh.interpolation(pde.solution, intertype='edge')
print(F1.shape)
F2 = self.mesh.interpolation(pde.solution, intertype='edgex')
print(F2.shape)
F3 = self.mesh.interpolation(pde.solution, intertype='edgey')
print(F3.shape)
F4 = self.mesh.interpolation(pde.solution, intertype='cell')
print(F4.shape)
end2 = time.time()
print('time of interpolation', end2 - start2)
def plane_quad_interpolation(self, p=2, fname='plane.vtu'):
from fealpy.pde.poisson_2d import CosCosData
from fealpy.mesh import LagrangeQuadrangleMesh
pde = CosCosData()
node = np.array([(0, 0), (0, 1), (1, 0), (1, 1)], dtype=np.float64)
cell = np.array([(0, 1, 2, 3)], dtype=np.int_)
mesh = LagrangeQuadrangleMesh(node, cell, p=p)
for i in range(4):
space = ParametricLagrangeFiniteElementSpace(mesh, p=p)
uI = space.interpolation(pde.solution)
mesh.nodedata['uI'] = uI[:]
error0 = space.integralalg.error(pde.solution, uI.value)
error1 = space.integralalg.error(pde.gradient, uI.grad_value)
print(error0, error1)
if i < 3:
mesh.uniform_refine()
mesh.to_vtk(fname=fname)
space = ConformingVirtualElementSpace2d(mesh, p=1)
A0, S0 = space.chen_stability_term()
A = space.stiff_matrix()
print("A:", A.toarray())
print("A0:", A0.toarray())
print("S0:", S0.toarray())
np.savetxt('A.txt', A.toarray(), fmt='%.2e')
np.savetxt('A0.txt', A0.toarray(), fmt='%.2e')
np.savetxt('S0.txt', S0.toarray(), fmt='%.2e')
if False:
h = 0.1
maxit = 1
pde = CosCosData()
box = pde.domain()
for i in range(maxit):
mesh = triangle(box, h / 2**(i - 1), meshtype='polygon')
space = ConformingVirtualElementSpace2d(mesh, p=1)
uh = space.function()
bc = BoundaryCondition(space, dirichlet=pde.dirichlet)
A0, S0 = space.chen_stability_term()
A0 = A0.toarray()
S0 = S0.toarray()
A = space.stiff_matrix()
F = space.source_vector(pde.source)
scale=1)
axes.quiver(space.ccenter[:, 0],
space.ccenter[:, 1],
A0[:, 0],
A0[:, 1],
angles='xy',
scale_units='xy',
scale=1)
plt.show()
node = np.array([(0, 0), (1, 0), (1, 1), (0, 1), (0.5, 0), (1, 0.4), (0.3, 1),
(0, 0.6), (0.5, 0.45)],
dtype=np.float)
cell = np.array([(0, 4, 8, 7), (4, 1, 5, 8), (7, 8, 6, 3), (8, 5, 2, 6)],
dtype=np.int)
pde = CosCosData()
mesh = QuadrangleMesh(node, cell)
mesh.uniform_refine(7)
space = QuadBilinearFiniteElementSpace(mesh)
uI = space.interpolation(pde.solution)
L2 = space.integralalg.L2_error(pde.solution, uI.value)
print("L2:", L2)
H1 = space.integralalg.L2_error(pde.gradient, uI.grad_value)
print("H1:", H1)
import matplotlib.pyplot as plt
from scipy.sparse import csr_matrix
import sys
import sympy
from mpl_toolkits.mplot3d import Axes3D
from fealpy.decorator import cartesian
from scipy.sparse.linalg import spsolve
from fealpy.boundarycondition import DirichletBC
from fealpy.pde.poisson_2d import CosCosData as PDE
from fealpy.tools.show import showmultirate, show_error_table
n = 10
p = 4
mf = MeshFactory()
mesh = mf.boxmesh2d([0, 1, 0, 1], nx=n, ny=n, meshtype='tri')
pde = PDE()
domain = pde.domain()
maxit = 4
errorType = [
'$|| u - u_h||_{\Omega,0}$', # L2 误差
'$||\\nabla u - \\nabla u_h||_{\Omega, 0}$'
] # H1 误差
errorMatrix = np.zeros((2, maxit), dtype=np.float)
NDof = np.zeros(maxit, dtype=np.float)
for i in range(maxit):
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)
def solve_poisson_2d(self, n=3, p=0, plot=True):
pde = CosCosData()
mesh = pde.init_mesh(n=n, meshtype='tri')
space = RaviartThomasFiniteElementSpace2d(mesh, p=p)
udof = space.number_of_global_dofs()
pdof = space.smspace.number_of_global_dofs()
gdof = udof + pdof
uh = space.function()
ph = space.smspace.function()
A = space.stiff_matrix()
B = space.div_matrix()
F1 = space.source_vector(pde.source)
AA = bmat([[A, -B], [-B.T, None]], format='csr')
if True:
F0 = -space.set_neumann_bc(pde.dirichlet)
FF = np.r_['0', F0, F1]
x = spsolve(AA, FF).reshape(-1)
uh[:] = x[:udof]
ph[:] = x[udof:]
error0 = space.integralalg.L2_error(pde.flux, uh)
def f(bc):
xx = mesh.bc_to_point(bc)
return (pde.solution(xx) - ph(xx))**2
error1 = space.integralalg.integral(f)
print(error0, error1)
else:
isBdDof = -space.set_dirichlet_bc(uh, pde.neumann)
x = np.r_['0', uh, ph]
isBdDof = np.r_['0', isBdDof, np.zeros(pdof, dtype=np.bool_)]
FF = np.r_['0', np.zeros(udof, dtype=np.float64), F1]
FF -= AA @ x
bdIdx = np.zeros(gdof, dtype=np.int)
bdIdx[isBdDof] = 1
Tbd = spdiags(bdIdx, 0, gdof, gdof)
T = spdiags(1 - bdIdx, 0, gdof, gdof)
AA = T @ AA @ T + Tbd
FF[isBdDof] = x[isBdDof]
x[:] = spsolve(AA, FF)
uh[:] = x[:udof]
ph[:] = x[udof:]
error0 = space.integralalg.L2_error(pde.flux, uh)
def f(bc):
xx = mesh.bc_to_point(bc)
return (pde.solution(xx) - ph(xx))**2
error1 = space.integralalg.integral(f)
print(error0, error1)
if plot:
box = [-0.5, 1.5, -0.5, 1.5]
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes, box=box)
#mesh.find_node(axes, showindex=True)
#mesh.find_edge(axes, showindex=True)
#mesh.find_cell(axes, showindex=True)
node = ps.reshape(-1, 2)
uv = uh.reshape(-1, 2)
axes.quiver(node[:, 0], node[:, 1], uv[:, 0], uv[:, 1])
plt.show()
from scipy.sparse.linalg import spsolve
from fealpy.pde.poisson_2d import CosCosData
from fealpy.mesh import MeshFactory
from fealpy.decorator import cartesian, barycentric
from fealpy.functionspace import RaviartThomasFiniteElementSpace2d
from fealpy.solver import SaddlePointFastSolver
p = int(sys.argv[1]) # RT 空间的次数
n = int(sys.argv[2]) # 初始网格部分段数
maxit = int(sys.argv[3]) # 迭代求解次数
pde = CosCosData() # pde 模型
box = pde.domain() # 模型区域
mf = MeshFactory() # 网格工场
for i in range(maxit):
mesh = mf.boxmesh2d(box, nx=n, ny=n, meshtype='tri')
space = RaviartThomasFiniteElementSpace2d(mesh, p=p)
udof = space.number_of_global_dofs()
pdof = space.smspace.number_of_global_dofs()
gdof = udof + pdof
print("step ", i, " with number of dofs:", gdof)
uh = space.function()
ph = space.smspace.function()
#!/usr/bin/env python3
#
import sys
import numpy as np
from scipy.sparse.linalg import spsolve
import matplotlib.pyplot as plt
from fealpy.pde.poisson_2d import CosCosData
from fealpy.functionspace import LagrangeFiniteElementSpace
from fealpy.boundarycondition import BoundaryCondition
pde = CosCosData()
print('test')
mesh = pde.init_mesh(n=7, meshtype='tri')
print('test')
space = LagrangeFiniteElementSpace(mesh, p=1)
print('test')
A = space.stiff_matrix()
print('test')
b = space.source_vector(pde.source)
print('test')
uh = space.function()
bc = BoundaryCondition(space, robin=pde.robin)
bc.apply_robin_bc(A, b)
uh[:] = spsolve(A, b).reshape(-1)
error = space.integralalg.L2_error(pde.solution, uh)
from fealpy.pde.poisson_2d import CosCosData as PDE import numpy as np from ShowCls import ShowCls from PoissonDGModel2d import PoissonDGModel2d from fealpy.mesh import MeshFactory as mf from fealpy.mesh import HalfEdgeMesh2d # from fealpy.mesh.mesh_tools import find_entity # import matplotlib.pyplot as plt # --- begin setting --- # d = 2 # the dimension p = 1 # the polynomial order n = 1 # the number of refine mesh maxit = 5 # the max iteration of the mesh pde = PDE() # create pde model pde.epsilon = -1 # setting the DG-scheme parameter # # epsilon may take -1, 0, 1, # # the corresponding DG-scheme is called symmetric interior penalty Galerkin (SIPG), # # incomplete interior penalty Galerkin (IIPG) and nonsymmetric interior penalty Galerkin (NIPG) pde.eta = 16 # setting the penalty parameter # # To get the optimal rate, one should choose the appropriate 'eta' # # according to the polynomial order 'p', 'epsilon' and mesh. # # error settings errorType = ['$|| u - u_h||_0$', '$||\\nabla u - \\nabla u_h||_0$'] errorMatrix = np.zeros((len(errorType), maxit), dtype=np.float) Ndof = np.zeros(maxit, dtype=np.int) # the array to store the number of dofs
def __init__(self):
self.pde = CosCosData()
self.mesh = self.pde.init_mesh(meshtype='quad')
self.space = QuadBilinearFiniteElementSpace(self.mesh)
from fealpy.functionspace import LagrangeFiniteElementSpace
from fealpy.boundarycondition import RobinBC
from fealpy.tools.show import showmultirate
p = int(sys.argv[1])
n = int(sys.argv[2])
maxit = int(sys.argv[3])
d = int(sys.argv[4])
if d == 2:
from fealpy.pde.poisson_2d import CosCosData as PDE
elif d == 3:
from fealpy.pde.poisson_3d import CosCosCosData as PDE
pde = PDE()
mesh = pde.init_mesh(n=n)
errorType = [
'$|| u - u_h||_{\Omega,0}$', '$||\\nabla u - \\nabla u_h||_{\Omega, 0}$'
]
errorMatrix = np.zeros((2, maxit), dtype=np.float)
NDof = np.zeros(maxit, dtype=np.float)
for i in range(maxit):
space = LagrangeFiniteElementSpace(mesh, p=p)
NDof[i] = space.number_of_global_dofs()
uh = space.function()
A = space.stiff_matrix()
import numpy as np import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D from fealpy.pde.poisson_2d import CosCosData as PDE from fealpy.functionspace import LagrangeFiniteElementSpace pde = PDE() mesh = pde.init_mesh(n=4, meshtype='tri') space = LagrangeFiniteElementSpace(mesh, 2) uI = space.interpolation(pde.solution) # 有限元空间的函数，同地它也是一个数组 bc = np.array([1 / 3, 1 / 3, 1 / 3], dtype=np.float64) val = uI(bc) # (NC, ) val = uI.value(bc) # (NC, ) gval = uI.grad_value(bc) #(NC, GD) L2error = space.integralalg.error(pde.solution, uI, q=5, power=2) H1error = space.integralalg.error(pde.gradient, uI.grad_value, q=5, power=2) print(H1error) fig = plt.figure() axes = fig.add_subplot(projection='3d') uI.add_plot(axes, cmap='rainbow') plt.show()
from fealpy.functionspace import LagrangeFiniteElementSpace
from fealpy.boundarycondition import NeumannBC
from fealpy.tools.show import showmultirate
p = 1
n = 2
maxit = 3
d = 4
if d == 2:
from fealpy.pde.poisson_2d import CosCosData as PDE
elif d == 3:
from fealpy.pde.poisson_3d import CosCosCosData as PDE
#pde = PDE()
pde = CosCosData()
mesh = pde.init_mesh(n=3)
errorType = [
'$|| u - u_h||_{\Omega,0}$', '$||\\nabla u - \\nabla u_h||_{\Omega, 0}$'
]
errorMatrix = np.zeros((2, maxit), dtype=np.float)
NDof = np.zeros(maxit, dtype=np.float)
for i in range(maxit):
space = LagrangeFiniteElementSpace(mesh, p=p)
NDof[i] = space.number_of_global_dofs()
uh = space.function()
A = space.stiff_matrix()
F = space.source_vector(pde.source)
def __init__(self, p=2, h=0.2):
self.pde = CosCosData()
