Frequency-Explicit A Posteriori Error Estimates for Discontinuous Galerkin Discretizations of Maxwell’s Equations

Abstract

SIAM Journal on Numerical Analysis, Volume 62, Issue 1, Page 400-421, February 2024.
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.