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We propose a new residual-based a posteriori error estimator fordiscontinuous Galerkin discretizations of time-harmonic Maxwell's equations infirst-order form. We establish that the estimator is reliable and efficient,and the dependency of the reliability and efficiency constants on the frequencyis analyzed and discussed. The proposed estimates generalize similar resultspreviously obtained for the Helmholtz equation and conforming finite elementdiscretization of Maxwell's equations. In addition, for the discontinuousGalerkin scheme considered here, we also show that the proposed estimator isasymptotically constant-free for smooth solutions. We also presenttwo-dimensional numerical examples that highlight our key theoretical findingsand suggest that the proposed estimator is suited to drive $h$- and$hp$-adaptive iterative refinements.

Frequency-explicit a posteriori error estimates for discontinuous Galerkin discretizations of Maxwell's equations