A residual-based a posteriori error estimator for the hp-finite element method for Maxwellʼs equations

We present a residual-based a posteriori error estimator for Maxwellʼs equations in the electric field formulation in three space-dimensions. The error estimator is constructed in terms of the residual of the considered problem and we prove upper and lower bounds in the energy norm, which are explicit in the mesh size and the polynomial degree of the ansatz space.