A least-squares method for axisymmetric div-curl systems

We present a negative-norm least-squares method for axisymmetric divcurl systems arising from Maxwell’s equations for electrostatics and magnetostatics in three dimensions. The method approximates the solution in a two-dimensional meridian plane. To achieve this dimension reduction, we must work with weighted spaces in cylindrical coordinates. In this setting, a stable pair of approximation spaces is developed and analyzed. We also report the results of some numerical experiments, which demonstrate a quasi-optimal convergence rate and a robustness with respect to the domain and coefficients.