Problem with ploting the solution

1

the équation is given by : \

-\epsilon u^{''}+ \lambda u^{'} = f \

the boundaries conditions are:\

u(1) = u(0) = 0 \
u is define in (0,1)
we have to find a numérical with finite élément P1 and P2
for P1 i have made this code :
‘’’ from future import print_function
import matplotlib.pyplot as plt
from fenics import *
import matplotlib.pyplot as plt
from dolfin import *
import numpy as np

from mshr import *

Parameters of the problem

nx = 10
epsilon = 0.1
lamda = 1.0
f = 1.0

Create mesh and define function space

mesh = UnitIntervalMesh(nx)

Q = FunctionSpace(mesh,“P”,1)

Define variational problem

plt.figure(figsize=(10, 5))
plot(mesh, title=“Maillage pour n = 10”)

Define the boundaries

u = TrialFunction(Q)

v = TestFunction(Q)

bord1 = ‘near(x[0], 0)’
bord2 = ‘near(x[0], 0)’

define boundary conditions

bcu_bord1 = DirichletBC(Q, Constant((0)), bord1)
bcu_bord2 = DirichletBC(Q, Constant((0)), bord2)
a = epsilon*inner(grad(u), grad(v))dx + lamdainner(u.dx(0), v)*dx
L = dot(f,v)*dx

solve the problem

bcu = [bcu_bord1, bcu_bord2]
w = Function(Q)
solve(a == L, w, bcu)

I want to plot the numérical solution of u but it doesnt work

2

You need to be more specific. What ways have you tried to plot the solution? Using the plot command and matplotlib.plyplot.show() or writing the data to pvd/XDMF using Paraview to visualize?

Do you get an error message?

3

Use triple quotes to make teh code readable. This seems to plot fine:

from dolfin import *

# Parameters of the problem
nx = 10
epsilon = 0.1
lamda = 1.0
f = 1.0

# Create mesh and define function space
mesh = UnitIntervalMesh(nx)

Q = FunctionSpace(mesh,"P",1)

# Define the boundaries
u = TrialFunction(Q)
v = TestFunction(Q)

bord1 = 'near(x[0], 0)'
bord2 = 'near(x[0], 0)'

# define boundary conditions
bcu_bord1 = DirichletBC(Q, Constant((0)), bord1)
bcu_bord2 = DirichletBC(Q, Constant((0)), bord2)
a = epsilon*inner(grad(u), grad(v))*dx + lamda*inner(u.dx(0), v)*dx
L = dot(f,v)*dx

# solve the problem
bcu = [bcu_bord1, bcu_bord2]
w = Function(Q)
solve(a == L, w, bcu)

import matplotlib.pyplot as plt
plt.figure(figsize=(10, 5))
plot(mesh, title="Maillage pour n=10")
plot(w)
plt.show()
# from vedo.dolfin import plot
# plot(w, xtitle="Maillage pour n=10", warpYfactor=0.8, lw=3, scalarbar=0)
2 Likes
4

Make sure to change the boundary condition

to this

bord2 = 'near(x[0], 1)'

as I pointed out in the original post