Residual based a posteriori error estimators for eddy current computation

We consider H(curl; Ohm)-elliptic problems that have been discretized by me ans of Nedelec's edge elements on tetrahedral meshes. Such problems occur i n the numerical computation of eddy currents. From the defect equation we d erive localized expressions that can be used as a posteriori error estimato rs to control adaptive refinement. Under certain assumptions on material pa rameters and computational domains, we derive local lower bounds and a glob al upper bound for the total error measured in the energy norm. The fundame ntal tool in the numerical analysis is a Helmholtz-type decomposition of th e error into an irrotational part and a weakly solenoidal part. Mathematics Subject Classification. 65N15, 65N30, 65N50.