A bug on boundary condition for i-tutorial unit 3.3.1, and related questions

Hello,

I am looking into traceoperator/geom_free implementation of DG.

My starting point is this i-tutorial ngsolve.org/docu/latest/i-tutorials/unit...hlight=traceoperator

In version 1, you are using the wall boundary condition . The numerical flux on the boundary is (Here maybe make a note that

p.Other()

returns p, not zero on the boundary edge, as it is sometimes confusing what the magic Other() operator is doing on domain boundary. See this discussion ngsolve.org/forum/ngspy-forum/28-inconsi...-in-bnd-integral#146 )

By increasing final time tend = 0.3, we find the boundary condition is indeed correctly implemented.

Then in Version 2, phat is the average on interior edges, but phat=p on boundary edges. Hence, to have a correct implementation of the boundary term Btr in block 11, I added the following hack to have the correct boundary condition:
With this correction, the version 2 results are identical to version 1 up to time tend=0.3. (Otherwise, we observe something wrong when wave hit the boundary)

Unfortunately, the same trick does not work for the geom_free version.
Do you have any suggestions to fix the boundary condition for Version 3?

Another question: does traceoperator and/or geom_free work on a periodic mesh?
I have some trouble getting consistent results on periodic mesh for the traceoperator.

Best,
Guosheng

I like the HDG-like implementation of an explicit DG scheme.
The traceop can be explicitly realized via a matrix-vector form (although the performance is a bit slower than traceop, but it handles the boundary condition correctly)
But the geom_free flag still does not work for a periodic facet fespace: the following operator shall allow for geom_free implementation, but it fails for a periodic facet fespace VF.