We consider H(curl;Ω)-elliptic problems that have been discretized by
means of Nédélec's edge elements on tetrahedral meshes. Such
problems
occur in the numerical computation of eddy currents. From the defect
equation we derive localized expressions that can be used
as a posteriori error estimators to control adaptive
refinement.
Under certain assumptions on material parameters and computational
domains, we derive local lower bounds and a global upper bound for the
total error measured in the energy norm. The fundamental tool in the
numerical analysis is a Helmholtz-type decomposition of the error into
an irrotational part and a weakly solenoidal part.