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A postprocessing technique for a discontinuous Galerkin discretization of time-dependent Maxwell's equations

Abstract : We present a novel postprocessing technique for a discontinuous Galerkin (DG) discretization of time-dependent Maxwell's equations that we couple with an explicit Runge-Kutta time-marching scheme. The postprocessed electromagnetic field converges one order faster than the unprocessed solution in the H(curl)-norm. The proposed approach is local, in the sense that the enhanced solution is computed independently in each cell of the computational mesh, and at each time step of interest. As a result, it is inexpensive to compute, especially if the region of interest is localized, either in time or space. The key ideas behind this postprocessing technique stem from hybridizable discontinuous Galerkin (HDG) methods , which are equivalent to the analyzed DG scheme for specific choices of penalization parameters. We present several numerical experiments that highlight the superconvergence properties of the postprocessed electromagnetic field approximation.
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https://hal.inria.fr/hal-02956882
Contributor : Théophile Chaumont-Frelet <>
Submitted on : Saturday, October 3, 2020 - 7:05:29 PM
Last modification on : Wednesday, October 14, 2020 - 3:53:35 AM

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  • HAL Id : hal-02956882, version 1

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Georges Nehmetallah, Théophile Chaumont-Frelet, Stéphane Descombes, Stéphane Lanteri. A postprocessing technique for a discontinuous Galerkin discretization of time-dependent Maxwell's equations. 2020. ⟨hal-02956882⟩

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