Interior penalty method for the indefinite time-harmonic Maxwell equations

In this paper, we introduce and analyze the interior penalty discontinuous Galerkin method for the numerical discretization of the indefinite time-harmonic Maxwell equations in the high-frequency regime. Based on suitable duality arguments, we derive a-priori error bounds in the energy norm and the L2-norm. In particular, the error in the energy norm is shown to converge with the optimal order [inline-graphic not available: see fulltext](hmin{s,ℓ}) with respect to the mesh size h, the polynomial degree ℓ, and the regularity exponent s of the analytical solution. Under additional regularity assumptions, the L2-error is shown to converge with the optimal order [inline-graphic not available: see fulltext](hℓ+1). The theoretical results are confirmed in a series of numerical experiments.