An Lp-DPG method for the convection–diffusion problem

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....

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2021-08, Vol.95, p.172-185
Main Authors: Li, Jiaqi, Demkowicz, Leszek
Format: Article
Language:English
Subjects:
Banach spaces
Convection
Convection-dominated diffusion
Discontinuous Petrov–Galerkin methods
Gibbs phenomenon
Hilbert space
Residual minimization
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Summary: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.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2020.08.013