Evaluation of boundary integral
 

Hi all,

I'm working on a Discontinuous Galerkin solver for the Euler equations and want to implement a discontinuity detector. This enables one to limit the solution only at discontinuities rather than everywhere, including at smooth extrema.

Specifically, I have chosen a detector developed at SCOREC. It involves a boundary integral at element interfaces of the jumps in the solution in adjacent elements.

However, the integral is only over the inflow portion (as seen from the element currently being considered for limiting).

[ The integral can be found in Eq. (8) of: http://www.scorec.rpi.edu/REPORTS/2003-3.pdf ]

I would like some suggestions on how to numerically evaluate such integrals. Each element boundary may have several and separate inflow regions (due to the high-order basis being used), so I'm not sure how to approach this.

I would appreciate it very much if I could get some pointers.

Thanks in advance, Aunola