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Pré-Publication, Document De Travail Année : 2023

Spectral correctness of the discontinuous Galerkin approximation of the first-order form of Maxwell's equations with discontinuous coefficients

Résumé

The paper analyzes the discontinuous Galerkin approximation of Maxwell's equations written in first-order form and with non-homogeneous magnetic permeability and electric permittivity. Although the Sobolev smoothness index of the solution may be smaller than 1/2 , it is shown that the approximation is spectrally correct. The convergence proof is based on a duality argument. One essential idea is that the smoothness index of the dual solution is always larger than 1/2 irrespective of the regularity of the material properties. Discrete involutions also play a key role in the analysis.
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Dates et versions

hal-04145808 , version 1 (29-06-2023)
hal-04145808 , version 2 (09-02-2024)

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  • HAL Id : hal-04145808 , version 1

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Alexandre Ern, Jean-Luc Guermond. Spectral correctness of the discontinuous Galerkin approximation of the first-order form of Maxwell's equations with discontinuous coefficients. 2023. ⟨hal-04145808v1⟩
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