It seems to me that those solutions work fine if the two meshes correspond to the same geometry. Maybe there is a solution written in the links you gave me but I am to new to FEniCS to understand them. But at least something compiles now, so maybe I can ask here for further problem. Or should I open new topic? Anyway, here is what confuses me. (I will open new topic if it is needed?)

This is perhaps some small working example:

```
from __future__ import print_function
from fenics import *
num_elem = 2
mesh2D = UnitSquareMesh(num_elem, num_elem)
space2D = FunctionSpace(mesh2D, 'P', 1)
mesh1D = IntervalMesh(num_elem, 0.0, 1.0)
space1D = FunctionSpace(mesh1D, 'P', 1)
f1Dexp = Expression('x[0]', degree = 1)
f1D = interpolate(f1Dexp, space1D)
f1Dp = f1D.vector().get_local()
coor = mesh1D.coordinates()
if coor.shape[0] == f1Dp.shape[0]:
for i in range(len(f1Dp)):
print ('f(%2g) = %g' % (coor[i][0], f1Dp[i]))
else:
print ('false dimension')
f2D = interpolate(f1D, space2D)
f2Dp = f2D.vector().get_local()
coor = mesh2D.coordinates()
if coor.shape[0] == f2Dp.shape[0]:
for i in range(len(f2Dp)):
print ('f(%2g, %2g) = %g' % (coor[i][0], coor[i][1], f2Dp[i]))
else:
print ('false dimension')
```

output is

```
f( 0) = 1
f(0.5) = 0.5
f( 1) = 0
f( 0, 0) = 0
f(0.5, 0) = 0
f( 1, 0) = 0.5
f( 0, 0.5) = 0
f(0.5, 0.5) = 0.5
f( 1, 0.5) = 1
f( 0, 1) = 0.5
f(0.5, 1) = 1
f( 1, 1) = 1
```

So two things I don’t understand. First, why are in the first three rows values flipped? I would expect to see

```
f( 0) = 0
f(0.5) = 0.5
f( 1) = 1
```

And the other thing is that ‘f(x, 0.5) = x’, and for second coordinate ‘0’ or ‘1’ there are some other values, I guess something that ‘interpolate’ choose to put there. And what I would like is that ‘f(x, 1) = x’, since my ‘mesh1D’ is representing the top side of a square ‘mesh2D’.

Is there a way to do this? Even manually would work for me. Also, the same behaviour exhibits when I change ‘num_elem = 4’ or ‘8’, I put ‘2’ just to make output more readable.