A stabilized finite element method on nonaffine grids for time-harmonic Maxwell's equations

A stabilized mixed finite element method is proposed for solving the time-harmonic Maxwell's equations, with the divergence constraint imposed by the multiplier in a weak sense. By a grad-div stabilization, for some lowest-order edge elements on nonaffine quadrilateral, hexahedral and prismatic grids, we prove a type of uniform convergence for the zero-frequency Maxwell's equations, then prove the well-posedness and the convergence for the time-harmonic Maxwell's equations. Numerical results confirm the theoretical results.