Constitutive inconsistency: rigorous solution of Maxwell equations based on a dual approach

A dual scheme is proposed, that correctly represents the electromagnetic fields as differential forms. A rigorous solution of Maxwell´s equations is obtained that satisfies both Ampere´s and Faraday´s laws. The solution of Maxwell´s equations derived from the numerical discretization of two complementary formulations is inconsistent with the constitutive laws. This inconsistency is used as an error estimator in a 3D adaptive refinement procedure resulting in very accurate solutions and reduced computational cost. A new error criterion, the dual constitutive error, consisting of two components: the electric error and the magnetic error, is introduced. Edge elements with tangential continuity are used giving no spurious solutions. The validity of the proposed technique is illustrated by an application to a loaded cavity