Discrete Compactness for Edge Elements in the Presence of Mixed Boundary Conditions

Abstract

It is shown---for the first time, to the best of the author's knowledge---that when the finite dimensional space sequence is generated by using Nedelec's edge elements of any order and of both families defined on tetrahedra, the so-called discrete compactness property holds true for Lipschitz polyhedra even in the presence of mixed boundary conditions. The family of meshes is not required to be quasi-uniform but just regular. A standard way to deal with general dielectric permittivities completes the picture.