A class of locally well-posed hybridizable discontinuous Galerkin methods for the solution of time-harmonic Maxwell's equations

We study locally well-posed hybridizable discontinuous Galerkin (HDG) methods for the numerical solution of the time-harmonic Maxwell's equations. The local well-posedness is obtained by introducing another facet variable closely related to the tangential component of the magnetic field, as compared to the initial formulation. With this newly introduced variable, we propose a class of generalized locally well-posed formulations which involves four parameters for flexibility. Numerical examples show that the approximate solutions converge to the exact solutions with optimal rates.