A pressure-robust stabilizer-free WG finite element method for the Stokes equations on simplicial grids

Date
2024-05-27
Journal Title
Journal ISSN
Volume Title
Publisher
Electronic Research Archive
Abstract
A pressure-robust stabilizer-free weak Galerkin (WG) finite element method has been defined for the Stokes equations on triangular and tetrahedral meshes. We have obtained pressure-independent error estimates for the velocity without any velocity reconstruction. The optimal-order convergence for the velocity of the WG approximation has been proved for the L2 norm and the H1 norm. The optimal-order error convergence has been proved for the pressure in the L2 norm. The theory has been validated by performing some numerical tests on triangular and tetrahedral meshes.
Description
This article was originally published in Electronic Research Archive. The version of record is available at: https://doi.org/10.3934/era.2024158. © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
Keywords
stabilizer-free, weak Galerkin, finite element, Stokes equations, pressure robust, tetrahedral meshes
Citation
Yan Yang, Xiu Ye, Shangyou Zhang. A pressure-robust stabilizer-free WG finite element method for the Stokes equations on simplicial grids[J]. Electronic Research Archive, 2024, 32(5): 3413-3432. doi: 10.3934/era.2024158