So far what I understand is that two neighbouring elements are conformal if their edges and faces match exactly, whereas with non-conformal elements this is not the case. For instance, h-refinement gives rise to hanging nodes, and h-nonconforming elements.
But then there is the concept of p-nonconforming. Note sure, but I think this applies for instance in DGFEM, where the weight functions are the roots of a polynomial and which do not match at the boundaries?
I would appreciate it if someone offered a simple explanation for this, particularly in the context of typical structured grids used in DGFEM, FEM and FVM.