Interior penalty method for the indefinite time-harmonic Maxwell equations

SummaryIn 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 (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 (hℓ+1). The theoretical results are confirmed in a series of numerical experiments.

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