I need to create a 2D mesh on a geometry in which 2 faces share one side. One face is vertical, the other horizontal. I have a mesh continuity problem, as shown in the image below.

Be sure that the edge is shared by the faces, otherwise it could be possible to set different parameters for the edges in both faces (as it seems to be the case).

If I had to do it, I would use the partition operation which ensures a shared edge for the two perpendicular faces here before meshing. SF677.py (2.0 KB)
HTH.

you can do a structured mesh as simple as that by simply adding the two of them to a compound and attending that salome does all the work, you should ‘cut’ you edge of the big rectangle that intersects the small one.
here I defined a global 1D hypothesis with 15 elements (all edges) and overwrite the ones in the green edge to be 30, so all edges in red are 15 and the edge in green is the somme of the elements in fugia + bleu.

this gives you a conformal mesh.
for this i created a group of edges (that is only the green edge) and then used for a sub mesh to define the number of elements. SF677_rev2.py (2,6 KB)
best regards