Frequency-explicit a posteriori error estimates for discontinuous Galerkin discretizations of Maxwell's equations

Théophile Chaumont-Frelet (1, 2) , Patrick Vega (3)

1 ATLANTIS - Modélisation et méthodes numériques pour le calcul d'interactions onde-matière nanostructurée
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 PUCV - Pontificia Universidad Católica de Valparaíso

We propose a new residual-based a posteriori error estimator for discontinuous Galerkin discretizations of time-harmonic Maxwell's equations in first-order form. We establish that the estimator is reliable and efficient, and the dependency of the reliability and efficiency constants on the frequency is analyzed and discussed. The proposed estimates generalize similar results previously obtained for the Helmholtz equation and conforming finite element discretization of Maxwell's equations. In addition, for the discontinuous Galerkin scheme considered here, we also show that the proposed estimator is asymptotically constantfree for smooth solutions. We also present two-dimensional numerical examples that highlight our key theoretical findings and suggest that the proposed estimator is suited to drive h and hp-adaptive iterative refinements.

Mots clés: a posteriori error estimates; hp-adaptivity; discontinuous Galerkin methods; high-frequency problems; Maxwell's equations

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Théophile Chaumont-Frelet, Patrick Vega. Frequency-explicit a posteriori error estimates for discontinuous Galerkin discretizations of Maxwell's equations. 2022. ⟨hal-03744230⟩