Alberto,

> I would like to have a few more details on the class FEInterfaceValues<dim>.
> since it is my feeling that  FEInterfaceValues<dim>
> might be conveniently used for interfaces, even out of DG methods.

Yes, I would think so.

> Specifically I'd like to figure out if this notion can be used without 
> recurring to the MeshWorker::mesh_loop,
> which I am not quite confident at present.

Note that we are not using the MeshWorker machinery but a single
function that contains the loops over the cells. The code of the
function is "relatively" easy to understand and you will appreciate
the logic for the following things you would have to deal with when
looping manually:
- assembling from the finer cell for interfaces with adaptive refinement
- correctly handling each facet once (or twice if desired) even in parallel
- handling of periodic boundaries

> I'd like to play autonomously with the class FEInterfaceValues<dim>
> but unfortunately I cannot grasp the notion of subface, which is apparently
> required by the reinit as in step 12:
>  fe_iv.reinit(cell, f, sf, ncell, nf, nsf);

With adaptivity you will need to pass the subface as returned by
neighbor_of_coarser_neighbor, otherwise it is
numbers::invalid_unsigned_int. See
https://github.com/dealii/dealii/blob/691ff4907964605dd21e94f06c880786af2cd612/tests/feinterface/fe_interface_values_03.cc#L94-L100
and
https://github.com/dealii/dealii/blob/691ff4907964605dd21e94f06c880786af2cd612/tests/feinterface/fe_interface_values_02.cc#L88-L93

> Can anyone address me some reading on this notion and how it is dealt with
> by the MeshWorker::mesh_loop ?

Take a look at the tests in tests/feinterface/:
https://github.com/dealii/dealii/tree/master/tests/feinterface

Many of them use FEInterfaceValues directly on a small test mesh.

-- 
Timo Heister
http://www.math.clemson.edu/~heister/

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