Interior penalty discontinuous Galerkin method for Maxwell's equations: optimal L2-norm error estimates

M. J. Grote, A. Schneebeli, D. Schotzau
<span title="2007-11-27">2007</span> <i title="Oxford University Press (OUP)"> <a target="_blank" rel="noopener" href="" style="color: black;">IMA Journal of Numerical Analysis</a> </i> &nbsp;
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
more &raquo; ... 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.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1093/imanum/drm038</a> <a target="_blank" rel="external noopener" href="">fatcat:zg2sraku3be3ja7fn44fow23xq</a> </span>
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