Domain decomposition for Stokes-Darcy, interface exchange term

Dear NGSolve community,

If we apply domain decomposition for the time-dependent Stokes-Darcy system. At each time step, we need to use the solution from the previous time step.

For example, if uh^D and uh^S represent the solution for Darcy region and Stokes region, respectively

We define the interface term for the Stokes region as follows:

Interface += InnerProduct(uh^D*n,mu)*ds(skeleton=True,definedon=mesh.Boundaries(“Interface”))

uh^D is the solution from the Darcy region from the previous time step. However, ds integrates for the Stokes region. I am wondering whether the order of degrees of freedom across the interface matches (because they are from two subdomains and if both are ordered counterclockwise, then they have opposite ordering across the interface).

Thank you very much.

Best regards,
Lina