Interior penalty method for the indefinite time-harmonic Maxwell equations |
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Authors: | Paul Houston Ilaria Perugia Anna Schneebeli Dominik Schötzau |
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Institution: | (1) Department of Mathematics, University of Leicester, Leicester, LE1 7RH, England;(2) Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy;(3) Department of Mathematics, University of Basel, Rheinsprung 21, 4051 Basel, Switzerland;(4) Mathematics Department, University of British Columbia, 121-1984 Mathematics Road, Vancouver, V6T 1Z2, Canada |
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Abstract: | Summary In 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,}) with respect to the mesh size h, the polynomial degree , and the regularity exponent s of the analytical solution. Under additional regularity assumptions, the L2-error is shown to converge with the optimal order (h+1). The theoretical results are confirmed in a series of numerical experiments.Supported by the EPSRC (Grant GR/R76615).Supported by the Swiss National Science Foundation under project 21-068126.02.Supported in part by the Natural Sciences and Engineering Council of Canada. |
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Keywords: | 65N30 |
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