import dolfin

import numpy as np

N = 4

mesh = dolfin.UnitSquareMesh(N, N, 'crossed')

scheme = 'CR' # 'TH' or 'CR'

if scheme == 'TH':

V = dolfin.VectorFunctionSpace(mesh, "CG", 2)

elif scheme == 'CR':

V = dolfin.VectorFunctionSpace(mesh, "CR", 1)

# define the boundary

def topleftbotright(x, on_boundary):

or np.fabs(x[0]) < dolfin.DOLFIN_EPS)

noslip = dolfin.Constant((0.0, 0.0))

bc = dolfin.DirichletBC(V, noslip, topleftbotright)

bcdict = bc.get_boundary_values()

bcinds = bcdict.keys()

innerinds = np.setdiff1d(range(V.dim()), bcinds)

bcinds = np.setdiff1d(range(V.dim()), innerinds)

# vector of -1

vvec = np.zeros(V.dim()) - 1

# set inner nodes to 1

vvec[innerinds] = 1

# assign to function

v = dolfin.Function(V)

v.vector().set_local(vvec)

# Evaluate CR at midpoints

mesh.init(1, 2)

midpoints = np.array([np.array([facet.midpoint().x(), facet.midpoint().y()])

for facet in dolfin.facets(mesh) if facet.exterior()])

U = np.zeros(len(midpoints))

V = np.zeros_like(U)

for i, mp in enumerate(midpoints):

U[i], V[i] = v(mp)

import matplotlib.tri as tri

import matplotlib.pyplot as plt

# Data for mesh

mesh_coordinates = mesh.coordinates().reshape((-1, 2))

triangles = np.asarray([cell.entities(0) for cell in dolfin.cells(mesh)])

triangulation = tri.Triangulation(mesh_coordinates[:, 0],

mesh_coordinates[:, 1],

triangles)

plt.figure()

plt.triplot(triangulation, color='b')

plt.quiver(midpoints[:, 0], midpoints[:, 1], U, V)

plt.xlim([-0.2, 1.2])

plt.ylim([-0.2, 1.2])

plt.show()