Summary: We introduce a discretization methodology for Maxwell equations based on Mimetic Finite Differences (MFD). Following the lines of the recent advances in MFD techniques [see F. Brezzi
et al., Comput. Methods Appl. Mech. Eng. 196, No. 37–40, 3682–3692 (2007; Zbl 1173.76370
)] and the references therein) and using some of the results of [F. Brezzi
and A. Buffa
, Scalar products of discrete differential forms, in preparation], we propose mimetic discretizations for several formulations of electromagnetic problems both at low and high frequency in the time-harmonic regime. The numerical analysis for some of the proposed discretizations has already been developed, whereas for others the convergence study is an object of ongoing research.