Spectral correctness of the discontinuous Galerkin approximation of the first-order form of Maxwell's equations with discontinuous coefficients - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2023

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

Abstract

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 converges strongly and is therefore spectrally correct. The convergence proof uses the notion of involution and is based on a deflated inf-sup condition and 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.
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Dates and versions

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

Identifiers

  • HAL Id : hal-04145808 , version 2

Cite

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-04145808v2⟩
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