Frequency-explicit a posteriori error estimates for discontinuous Galerkin discretizations of Maxwell's equations
| Autor: | Chaumont-Frelet, Théophile, Vega, Patrick |
|---|---|
| Přispěvatelé: | Modélisation et méthodes numériques pour le calcul d'interactions onde-matière nanostructurée (ATLANTIS), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Laboratoire Jean Alexandre Dieudonné (LJAD), Pontificia Universidad Católica de Valparaíso (PUCV) |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
a posteriori error estimates
discontinuous Galerkin methods Mathematics - Analysis of PDEs Maxwell's equations FOS: Mathematics high-frequency problems [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] hp-adaptivity Numerical Analysis (math.NA) Mathematics - Numerical Analysis [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] Analysis of PDEs (math.AP) |
| Popis: | 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 constant-free 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. arXiv admin note: substantial text overlap with arXiv:2009.09204 |
| Databáze: | OpenAIRE |
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