Matrix properties of a vector potential cell method for magnetostatics

In this paper, a proof of the symmetry of the system matrix arising in a class of vector potential cell methods with non-symmetric material matrices is presented. Some remarks on how to construct other schemes with symmetric system matrices are also presented. The explicit expression of the matrix entries derived in order to prove the symmetry is also used to show that this matrix is identical to the one arising in the standard edge finite-element method. Finally, some remarks on discrete regularizations of these formulations are given.