Yang, YanYe, XiuZhang, Shangyou2024-06-102024-06-102024-05-27Yan 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.20241582688-1594https://udspace.udel.edu/handle/19716/34456This 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)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.en-USAttribution 4.0 Internationalstabilizer-freeweak Galerkinfinite elementStokes equationspressure robusttetrahedral meshesArticle