An HDG method for Maxwell’s equations in heterogeneous media

Abstract We analyze a hybridizable discontinuous Galerkin (HDG) method for the time harmonic Maxwell’s equations arising from modeling photovoltaic solar cells. The problem is set in an inhomogeneous domain with a polyhedral connected boundary and the divergence-free condition is imposed using a Lagrange multiplier. We prove the HDG scheme is well-posed up to some frequencies and derive a stability estimate. In particular, we prove that the method is absolutely stable without any mesh constraint even for solutions with low regularity, when the stabilization parameters are chosen as purely imaginary. Moreover, when the solution has enough regularity, we show that the L 2 -norm of the error of the approximation in the electric and magnetic fields, are of order h k + 1 and h k + 1 ∕ 2 , where k is the polynomial degree of the local approximation spaces. Numerical examples are shown to validate the theory.