Fipy: problems with flux=0 constraints

diff_prob1.py

from fipy import *
from fipy.tools.numerix import exp

# Basic Setup
nx = 200; dx = 0.01; L = nx * dx
A = 15.0; B = 0.1; phi_0 = 1.; D = 1.
mesh = Grid1D(nx = nx, dx = dx)


# Cell variable and constrains
phi = CellVariable(name="phi", mesh=mesh, value=phi_0 )
phi.faceGrad.constrain(0., where=mesh.facesLeft)
# CHANGE ME!
#phi.faceGrad.constrain(0., where=mesh.facesRight) # NOT REALISTIC RESULT
phi.constrain(phi_0, where=mesh.facesRight) # REALISTIC RESULT


# Diffusion and Source terms
# Following: http://www.mail-archive.com/[email protected]/msg02119.html
diffusion_term = DiffusionTerm( coeff=D, var=phi )
x = mesh.getCellCenters()[0]
source_term = A * exp(-A * x) + B * (phi**2 - phi_0 **2)
equation = 0 == diffusion_term + source_term


# Solver
equation.solve()
viewer = Viewer( vars = (phi,) )
viewer.plot()
raw_input("Press <return> to proceed...")

For latex version of the equations here see, http://i.imgur.com/mCcX2.

When both the left and right side have zero flux constrains I don't think the solution is correct.