Dear colleagues;
I want to solve \Delta \psi=f (stream function formulation for radial injection) over a square minus a circle domain. I want to make a jump over the internal boundary shown as a blue dash line, i.e., \psi_{above}=\psi_{blow}+c.
Thus using a DG formulation, with B.C., grad \psi .n=0 at all boundaries, I have:
- \int_\Omega grad \psi grad \nu dA+ \sum \limits _{c \epsilon f_{i}} \int_{\delta T} { grad \psi^+ grad \nu^{+}- grad \psi^- grad \nu^{-} } ndS=\int_\Omega f \nu dA
Now I am wondering how I can push the constraint that I want, i.e., \psi_{above}=\psi_{below}+const, into the formulation.
I use P2 elements for \psi and P1dc for f, and indeed I want to create two different \psi values on both sides of the internal boundary as:
Any thoughts would be appreciated;