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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.
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.
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