Boundary Integral with Sources on Boundary

[kamensky]

I’m not sure what exactly is meant by a source on the boundary here, although I’ll point out that direct evaluation of the flux on boundaries is, generally, not very accurate, and there is a fairly old post-processing technique to get boundary flux estimates that converge faster than direct evaluation and satisfy the conservation law exactly. See my old posts here, and, for conservative flux estimates on subsets of the boundary, here.