Spectral Correctness of the Simplicial Discontinuous Galerkin Approximation of the First-Order Form of Maxwell’s Equations with Discontinuous Coefficients
Alexandre Ern, Jean‐Luc Guermond · SIAM Journal on Numerical Analysis · 2025
Abstract. The paper analyzes the discontinuous Galerkin approximation of Maxwell’s equations written in first-order form and with nonhomogeneous magnetic permeability and electric permittivity. Although the Sobolev smoothness index of the solution may be smaller than [Formula: see text], 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 [Formula: see text] irrespective of the regularity of the material properties.