An Lp-DPG method for the convection–diffusion problem. (1st August 2021)

• Record Type: Journal Article
• Authors: Li, Jiaqi; Demkowicz, Leszek
• Is Part Of: Computers & mathematics with applications. Volume 95(2021)
• Page Start: 172
• Page End: 185
• Publication Date: 2021-08-01
• Subjects: Discontinuous Petrov–Galerkin methods -- Residual minimization -- Banach spaces -- Convection-dominated diffusion; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2020.08.013
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: Following Muga and van der Zee (Muga and van der Zee, 2015), we generalize the standard Discontinuous Petrov–Galerkin (DPG) method, based on Hilbert spaces, to Banach spaces. Numerical experiments using model 1D convection-dominated diffusion problem are performed and compared with Hilbert setting. It is shown that Banach-based method gives solutions less susceptible to Gibbs phenomenon. h-adaptivity is implemented with the help of the error representation function as error indicator.