A robust a posteriori error estimator for divergence-conforming discontinuous Galerkin methods for the Oseen equation

• Verfasst von: Khan, Arbaz [VerfasserIn]
• Verfasst von: Kanschat, Guido [VerfasserIn]
• Titel: A robust a posteriori error estimator for divergence-conforming discontinuous Galerkin methods for the Oseen equation
• Verf.angabe: Arbaz Khan and Guido Kanschat
• E-Jahr: 2020
• Jahr: February 6, 2020
• Umfang: 27 S.
• Fussnoten: Gesehen am 27.07.2020
• Titel Quelle: Enthalten in: Society for Industrial and Applied MathematicsSIAM journal on numerical analysis
• Ort Quelle: Philadelphia, Pa. : SIAM, 1966
• Jahr Quelle: 2020
• Band/Heft Quelle: 58(2020), 1, Seite 492-518
• ISSN Quelle: 1095-7170
• DOI: doi:10.1137/18M1169072
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: a posteriori error estimates
• Sach-SW: approximations
• Sach-SW: divergence-conforming DG methods
• Sach-SW: Oseen equations
• K10plus-PPN: 172558946X

Abstract

In this paper, a robust a posteriori error estimator for divergence-conforming discontinuous Galerkin methods for the Oseen equation is presented. Upper and local lower bounds for the velocity-pressure error in terms of the energy norm and a seminorm associated with the convective term are derived. We prove that the ratio of upper and lower bounds is independent of the Reynolds number. Thus the proposed estimator is fully robust. Specific numerical experiments are discussed to validate the theoretical results.