[Dune] Trace-Meshes like ALBERTA "Sub-Meshes" (which are trace meshes, i.e. codim 1)

[Christian Engwer]

Dear Claus-Justus,

> However, problems arise when it comes to adaptivity in the context of
> conforming meshes. Ideally, this should work in both directions, and
> there the interesting part of the story starts. Does an arbitrary
> adaptation of the trace-mesh leads to an admissible refinement of the
> bulk mesh? What about matching degrees of freedom and finite element
> spaces (such that both finite element spaces remain "standard" in a
> to-be-settled context)? Ideally, one would hope to have a match
> between the trace-mesh and any of the existing dune-grid implementations
> such that the potentially distinct refinement algorithms of Nd and
> (N+1)d are compatible. For which of the existing meshes does this hold?

Following the meta-grid philosophy, the trace-grid would never do the
refinement on it's own, but mark the bulk-entity for refinement. After
the adaptation we obtain the refinement of the trace entity.

I'd imagine the following:

bulk.preAdapt();
trace.preAdapt()

// mark via a trace entity
trace.mark(traceentity);
// ... which will call
// trace.bulkGrid().mark(trace.bulkEntity(traceentity))

// mark an other entity via the bulk grid
bulk.mark(bulkentity);

bulk.postAdapt();
trace.postAdapt(); // this call will include the update of the trace grid

To answer you other questions... I don't know of anybody actually
writing such a mesh. There have been several attempts to provide
similar functionality in special contextes and it all boils down to
... it is simple for conforming functionspaces, as you don't have to
deal with intersections and just ommit them, but otherwise the missing
intersections will require a substential effort.

Ciao
Christian