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

Vega, Patrick

Keywords: a posteriori error estimates discontinuous Galerkin methods, high-frequency problems, Maxwell’s equations

Abstract

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 discretizations of Maxwell's equations. In addition, for the discontinuous Galerkin scheme considered here, we also show that the proposed estimator is asymptotically constant-free for smooth solutions.

Más información

Título según WOS: FREQUENCY-EXPLICIT A POSTERIORI ERROR ESTIMATES FOR DISCONTINUOUS GALERKIN DISCRETIZATIONS OF MAXWELL'S EQUATIONS
Volumen: 62
Número: 1
Fecha de publicación: 2024
Página de inicio: 400
Página final: 421
Idioma: English
URL: https://epubs.siam.org/doi/abs/10.1137/22M1516348
DOI:

10.1137/22M1516348

Notas: ISI