DG bases with DGLocalFiniteElement
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 the
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.