A quasi-optimal test norm for a DPG discretization of the convection-diffusion equation. (15th July 2021)

• Record Type: Journal Article
• Authors: Metcalfe, Stephen; Nadarajah, Siva
• Is Part Of: Computers & mathematics with applications. Volume 94(2021)
• Page Start: 60
• Page End: 75
• Publication Date: 2021-07-15
• Subjects: Discontinuous Petrov-Galerkin (DPG) -- Convection-diffusion -- Test norm; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.04.020
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this work, we propose a new quasi-optimal test norm for a discontinuous Petrov-Galerkin (DPG) discretization of the ultra-weak formulation of the convection-diffusion equation. We prove theoretically that the proposed test norm leads to bounds between the target norm and the energy norm induced by the test norm which have favorable scalings with respect to the diffusion parameter when compared with existing results for other test norms from the literature. We conclude with numerical experiments to confirm our theoretical results.