We prove the discrete compactness property of the edge elements of any order on a class
of anisotropically refined meshes on polyhedral domains. The meshes, made up of
tetrahedra, have been introduced in [Th. Apel and S. Nicaise, Math. Meth. Appl.
Sci. 21 (1998) 519–549]. They are appropriately graded near
singular corners and edges of the polyhedron.