In this paper we prove the discrete compactness property for a discontinuous Galerkin approximation of Maxwell's system on quite general tetrahedral meshes. As a consequence, a discrete Friedrichs inequality is obtained and the convergence of the discrete eigenvalues to the continuous ones is deduced using the theory of collectively compact operators. Some numerical experiments confirm the theoretical predictions.

Two new time-dependent versions of div-curl results in a bounded domain $\Omega \subset {ℝ}^3$ are presented. We study a limit of the product $v_k{w}_k$, where the sequences $v_k$ and $w_k$ belong to ${Ł}_2\left(\Omega \right)$. In Theorem 2.1 we assume that $\nabla \times v_k$ is bounded in the $L_p$-norm and $\nabla ·w_k$ is controlled in the $L_r$-norm. In Theorem 2.2 we suppose that $\nabla \times w_k$ is bounded in the $L_p$-norm and $\nabla ·w_k$ is controlled in the $L_r$-norm. The time derivative of $w_k$ is bounded in both cases in the norm of $-1\left(\Omega \right)$. The convergence (in the sense of distributions) of $v_k{w}_k$ to the product $vw$ of weak limits...

Three non-overlapping domain decomposition methods are proposed for the numerical approximation of time-harmonic Maxwell equations with damping (i.e., in a conductor). For each method convergence is proved and, for the discrete problem, the rate of convergence of the iterative algorithm is shown to be independent of the number of degrees of freedom.

Three non-overlapping domain decomposition methods are proposed for the numerical approximation of time-harmonic Maxwell equations with damping (i.e., in a conductor). For each method convergence is proved and, for the discrete problem, the rate of convergence of the iterative algorithm is shown to be independent of the number of degrees of freedom.