Dear FEniCS community,

I would like to solve a steady PDE on the unit square whose boundary conditions have been obtained from the (boundary) solution of another PDE (on the same mesh) solved again in the FEniCS environment (in serial). I have tried various ways, including the following approach.

I have computed the first PDE and using the following snippet tried to obtain the boundary data:

```
xpoints = np.linspace(0, 1, 40)
xlinepoints = [(xp_, 1.0) for xp_ in xpoints]
u_alongx = np.array([u(linep) for linep in xlinepoints])
```

where u is the solution of the first PDE whose boundary data will be used. I found the solutions along the boundaries (e.g., in the above snippet, it is given for y=1.0) and later tried to impose the data somehow along the same boundary (edge) for the new PDE. Unfortunately, I could not achieve it.

To make it clearer, I have solved a simple (steady, linear) PDE (in the FEniCS 2019.2.0.dev0 ecosystem) illustrated in the following figure. Now, I would like to solve another PDE on the same mesh whose solution will accept the boundary conditions along x=1 and y=1 from the previously computed (below-given) solution. The other two boundary conditions will be zero because these are also zero along x=0 and y=0.

Could you please help me out to find my way?

Thank you.