# Unexpected behavior of surface integral at internal boundary

**URL:** <https://fenicsproject.discourse.group/t/unexpected-behavior-of-surface-integral-at-internal-boundary/12254>\
**Category:** General\
**Created:** [September 21, 2023, 12:40am UTC](https://fenicsproject.discourse.group/t/unexpected-behavior-of-surface-integral-at-internal-boundary/12254 "2023-09-21T00:40:18Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![sbhasan](https://avatars.discourse-cdn.com/v4/letter/s/ed655f/32.png) [@sbhasan](https://fenicsproject.discourse.group/u/sbhasan)\
**Post date:** [September 21, 2023, 12:40am UTC](https://fenicsproject.discourse.group/t/unexpected-behavior-of-surface-integral-at-internal-boundary/12254/1 "2023-09-21T00:40:18Z")

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Hi,

I am working with dolfinx 0.6.0 installed through conda and presently struggling with unexpected behavior of the surface integral over internal boundaries for my use case. I know that ‘ds’ is for external boundaries while ‘dS’ is for internal ones. However, puzzlingly I am getting a non-zero integral with ‘ds’ on an internal boundary (‘dS’ being zero then).

I am not simplifying the geometry for the MWE because then I do not see this behavior. I would appreciate if someone willing to help executes the MWE below with the mesh file from [this link](https://simaxis-my.sharepoint.com/:u:/g/personal/s_b_hasan_simaxis_co/EXFhhLnZTxlHuPzeJ6e3rrUBd2EP_A4-gESx81CevK-I9w?e=TeZdaH) placed in the same folder.

```auto
import dolfinx, gmsh, petsc4py, mpi4py, ufl, time
from dolfinx.io import gmshio

gmsh_file = 'perm_magnet.msh'

gmsh.initialize()
gmsh.model.add("modelo_1")
gmsh.option.setNumber("General.Terminal", 1)
in_geom = gmsh.merge("perm_magnet.msh")
mpi_rank = 0 
mesh, ct, ft = gmshio.model_to_mesh(gmsh.model, mpi4py.MPI.COMM_WORLD, mpi_rank)

internal_surf_tag = 17 # internal surface, seen visually in gmsh

facet_tag = dolfinx.mesh.meshtags(mesh, mesh.topology.dim-1, ft.indices, ft.values)
ds = ufl.Measure('ds', domain=mesh, subdomain_data=facet_tag)
dS = ufl.Measure('dS', domain=mesh, subdomain_data=facet_tag)
n = ufl.FacetNormal(mesh)
flux_ds = dolfinx.fem.form(1 * ds(internal_surf_tag))
flux_dS = dolfinx.fem.form(1 * dS(internal_surf_tag))
print("Integral using ds:", dolfinx.fem.assemble.assemble_scalar(flux_ds))
print("Integral using dS:", dolfinx.fem.assemble.assemble_scalar(flux_dS))

```

I will sincerely appreciate help finding the mistake.

Thanks!

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<div class="post-metadata">

**Author:** ![sbhasan](https://avatars.discourse-cdn.com/v4/letter/s/ed655f/32.png) [@sbhasan](https://fenicsproject.discourse.group/u/sbhasan)\
**Post date:** [September 21, 2023, 2:03am UTC](https://fenicsproject.discourse.group/t/unexpected-behavior-of-surface-integral-at-internal-boundary/12254/2 "2023-09-21T02:03:05Z")

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Upon further look, turns out that I did not fragment the two adjacent objects in gmsh which caused this behavior.