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Interior penalty discontinuous Galerkin method for Maxwell's equations: optimal L2-norm error estimates
<span title="2007-11-27">2007</span>
<i title="Oxford University Press (OUP)">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2aq3wotb6jei3irc23tkqob3ee" style="color: black;">IMA Journal of Numerical Analysis</a>
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We consider the symmetric, interior penalty discontinuous Galerkin (DG) method for the time-dependent Maxwell's equations in second-order form. In Grote et al. (2007, J. Comput. Appl. Math., 204, 375-386), optimal a priori estimates in the DG energy norm were derived, either for smooth solutions on arbitrary meshes or for low-regularity (singular) solutions on conforming, affine meshes. Here, we show that the DG methods are also optimally convergent in the L 2 -norm, on tetrahedral meshes and
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... r smooth material coefficients. The theoretical convergence rates are validated by a series of numerical experiments in two-space dimensions, which also illustrate the usefulness of the interior penalty DG method for timedependent computational electromagnetics.
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