Robust a posteriori error estimation for the Maxwell equations

We consider a robust a posteriori error estimator of residual type for the Maxwell equations in a bounded two (and three) dimensional domain. The continuous problem is approximated using conforming approximated spaces. The main goal is to express the lower and upper bounds with respect to appropriate norms. For that purpose, a new interpolant of Clément/Nédélec type is introduced and some interpolation error estimates are proved. Numerical tests are presented which confirm our theoretical results.