Dear Praveen,

> The documentation says that GaussLobatto node-based FE_TraceQ will be
> implemented in future. Is there any estimate on when this will be
> available ?
The documentation is outdated. Indeed, FE_TraceQ is based on the nodes
of the Gauss-Lobatto quadrature formula. See the code in
source/fe/fe_trace.cc, constructor call. We somehow forgot to update the
documentation. I will open a pull request.

> In Interior Embedded DG (IEDG) scheme, you need trace spaces which are
> continuous on interior faces but discontinuous on boundary faces. Is
> there a plan to implement such a space in deal.II ?
Please help me understand your question: You want to have the behavior
of FE_TraceQ on interior faces and FE_FaceQ at the boundary? Having this
kind of distinction is not easily possible because of the way elements
are organized in deal.II. We logically assign degrees of freedom to the
vertices, edges, quads and hexes of the elements. In the case of
FE_TraceQ in 3D, linear functions live on vertices only, whereas for
quadratics and higher you also put nodes on the midpoints of edges and
the quads. For FE_FaceQ, we put all degrees of freedom on the quads,
even though the support points of linears is still at the vertex
location. This way, we get duplicated degrees of freedom.

If you want to construct such a space, you will need to do some manual
labor: My suggestion would be that you build FE_FaceQ and then manually
find constraints that put the vertices (and edges in 3D) that sit on the
same physical position to the same degree of freedom. It should be
pretty straight-forward to do so.

Best,
Martin

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