DG bases with DGLocalFiniteElement
Currently, LagrangeDGNode
is just an alias of a LagrangeNode
. If you just look at an element locally, this is totally fine since the same local basis functions are used. But interpreted in the global basis, the connectivity of the local basis functions should be encoded in the grid entity the local basis functions are associated with. This is not the case when implementing LagrangeDG
with theLagrangeNode
.
I propose to replace the LagrangeLocalFiniteElement
(used currently in the LagrangeNode
for runtime order bases) with DGLocalFiniteElement<LagrangeLocalFiniteElement>
in the LagrangeDGNode
. This wrapper factory maps the lagrange local keys to a local key where all local DOFs are associated to the element of codim=0 instead of the individual subentities.
The implementation should be straightforward. Maybe it is possible to add a similar strategy for the PQKLocalFiniteElementCache
as well.