Integrating a discontinuous field over a curve bounding a regio,n

variational formulation
1

Hello, I have a discontinuous field U

W = functionspace(mesh, ("DG", 0, (mesh.geometry.dim, )))
U = Function(W)

I wish to integrate over a curve consisting of mesh edges.
This curve bounds a region, which are both tagged, using gmsh physical tags.

I have to decide whether to integrate U("+"), or U("-") using the following measure

dS = Measure("dS", domain=mesh, subdomain_data=facet_tags, sudomain_id=curve2integrate)

Is "+" pointing inward or outward the region bounded by the curve?

2

See for instance: Add one-sided integration example as example of custom integration · Issue #158 · jorgensd/dolfinx-tutorial · GitHub
as explained in: Wrong FacetNormal vector on internal boundaries - #3 by sbhasan or Hyperelastic deformation with applied pressue on internal surface - #2 by dokken

3

Thanks for your insight.

In my case, the restriction (last link) was the solution I needed.