I am solving an elliptic boundary value problem on a subset of the rectangle [-1,1]x[-1,1]. The domain contains the line segment x=0, however this does not need to be a part of the boundary, so it is not aligned with the facets by default.
I want to compute the flux of a solution function across the line segment x=0. I know from the tutorial how to compute fluxes over boundary elements. However, I am not sure whether making the line a boundary element is necessary in this case. Nor am I sure how to insert it, since simply inserting the line into the mesh will cause degrees of freedom to conflict, as would naively gluing rectangles together. Can you offer any suggestions on how to compute this flux?