A negative-norm least-squares method for time-harmonic Maxwell equations (Q662071)

The author presents a negative-norm least-squares method for time-harmonic axisymmetric Maxwell problems, which decouple in cylindrical coordinates into independent two-dimensional problems. The analysis is performed in weighted Sobolev spaces based on the degenerate radial weighting. The existence and uniqueness of solutions of the continuous and discrete formulation are established. The author proves the stability of the least-squares method and derives quasi-optimal error estimates in negative norms. The performance of the method is demonstrated in numerical experiments for problems with continuous and discontinuous material properties.