Hi everyone,

Following the great Dolfinx Tutorials I tried to evaluate a function at one point in parallel. However, I noticed that points which are in the border of the mesh partition may have a different value depending on the process.

Consider this:

```
import dolfinx
from mpi4py import MPI
import numpy as np
#
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
# define mesh
mesh = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, 10, 10)
# define function space
V = dolfinx.fem.FunctionSpace(mesh, ("CG", 1))
# function
foo = dolfinx.fem.Function(V)
foo.interpolate(lambda x: rank * np.ones(x[0].shape))
# xdmf file
xdmf = dolfinx.io.XDMFFile(comm, "scratches/foo.xdmf", "w")
xdmf.write_mesh(mesh)
xdmf.write_function(foo)
# select a point in the mesh in the border between the two processes
rand_global_point = [0.5, 0.5, 0.]
# get bbt for the mesh
mesh_bbt = dolfinx.geometry.BoundingBoxTree(mesh, mesh.topology.dim)
# convert point in array with one element
points_list_array = np.array([rand_global_point, ])
# for each point, compute a colliding cells and append to the lists
points_on_proc = []
cells = []
cell_candidates = dolfinx.geometry.compute_collisions(mesh_bbt, points_list_array) # get candidates
colliding_cells = dolfinx.geometry.compute_colliding_cells(mesh, cell_candidates, points_list_array) # get actual
for i, point in enumerate(points_list_array):
if len(colliding_cells.links(i)) > 0:
cc = colliding_cells.links(i)[0]
points_on_proc.append(point)
cells.append(cc)
# convert to numpy array
points_on_proc = np.array(points_on_proc)
cells = np.array(cells)
if len(points_on_proc) > 0:
print(f"r{rank}: \t * foo.eval(points = {points_on_proc}, cells = {cells}) = "
f"{foo.eval(points_on_proc, cells)}")
```

What I get running with `mpirun -n 2 `

is:

```
r1: * foo.eval(points = [[0.5 0.5 0. ]], cells = [104]) = [1.]
r0: * foo.eval(points = [[0.5 0.5 0. ]], cells = [24]) = [0.]
```

However, looking at my mesh in Paraview the correct value should be 0., regardless the process (the point Iām testing is [0.5, 0.5]):

Am I doing something wrong?