A stabilizer-free pressure-robust finite element method for the Stokes equations
Author(s) | Ye, Xiu | |
Author(s) | Zhang, Shangyou | |
Date Accessioned | 2021-12-22T20:41:11Z | |
Date Available | 2021-12-22T20:41:11Z | |
Publication Date | 2021-04-08 | |
Description | This article was originally published in Advances in Computational Mathematics. The version of record is available at: https://doi.org/10.1007/s10444-021-09856-9 | en_US |
Abstract | In this paper, we introduce a new finite element method for solving the Stokes equations in the primary velocity-pressure formulation using H(div) finite elements to approximate velocity. Like other finite element methods with velocity discretized by H(div) conforming elements, our method has the advantages of an exact divergence-free velocity field and pressure-robustness. However, most of H(div) conforming finite element methods for the Stokes equations require stabilizers to enforce the weak continuity of velocity in tangential direction. Some stabilizers need to tune penalty parameter and some of them do not. Our method is stabilizer free although discontinuous velocity fields are used. Optimal-order error estimates are established for the corresponding numerical approximation in various norms. Extensive numerical investigations are conducted to test accuracy and robustness of the method and to confirm the theory. The numerical examples cover low- and high-order approximations up to the degree four, and 2D and 3D cases. | en_US |
Sponsor | Xiu Ye was supported in part by the National Science Foundation Grant DMS-1620016. | en_US |
Citation | Ye, X., Zhang, S. A stabilizer-free pressure-robust finite element method for the Stokes equations. Adv Comput Math 47, 28 (2021). https://doi.org/10.1007/s10444-021-09856-9 | en_US |
ISSN | 1572-9044 | |
URL | https://udspace.udel.edu/handle/19716/29914 | |
Language | en_US | en_US |
Publisher | Advances in Computational Mathematics | en_US |
Keywords | Weak gradient | en_US |
Keywords | Finite element methods | en_US |
Keywords | The Stokes equations | en_US |
Keywords | Pressure-robust | en_US |
Title | A stabilizer-free pressure-robust finite element method for the Stokes equations | en_US |
Type | Article | en_US |
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