Open AccessWeak Galerkin method for the Stokes equations with damping
Author(s) -
Hui Peng,
Qingfeng Zhai
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021112
Subject(s) - polygon mesh , galerkin method , stokes problem , mathematics , finite element method , discontinuous galerkin method , scheme (mathematics) , error analysis , mathematical analysis , order (exchange) , physics , geometry , thermodynamics , finance , economics
In this paper, we introduce the weak Galerkin (WG) finite element method for the Stokes equations with damping. We establish the WG numerical scheme on general meshes and prove the well-posedness of the scheme. Optimal error estimates for the velocity and pressure are derived. Furthermore, in order to accelerate the WG algorithm, we present a two-level method and give the corresponding error estimates. Finally, some numerical examples are reported to validate the theoretical analysis.