A pressure-robust stabilizer-free WG finite element method for the Stokes equations on simplicial grids
| Author(s) | Yang, Yan | |
| Author(s) | Ye, Xiu | |
| Author(s) | Zhang, Shangyou | |
| Date Accessioned | 2024-06-10T17:57:25Z | |
| Date Available | 2024-06-10T17:57:25Z | |
| Publication Date | 2024-05-27 | |
| 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) | |
| 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. | |
| Sponsor | Yan Yang is supported in part by the Program of Sichuan National Applied Mathematics Center, No. 2023-KFJJ-01-001. | |
| 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 | |
| ISSN | 2688-1594 | |
| URL | https://udspace.udel.edu/handle/19716/34456 | |
| Language | en_US | |
| Publisher | Electronic Research Archive | |
| dc.rights | Attribution 4.0 International | en |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
| Keywords | stabilizer-free | |
| Keywords | weak Galerkin | |
| Keywords | finite element | |
| Keywords | Stokes equations | |
| Keywords | pressure robust | |
| Keywords | tetrahedral meshes | |
| Title | A pressure-robust stabilizer-free WG finite element method for the Stokes equations on simplicial grids | |
| Type | Article |
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