A stabilizer-free pressure-robust finite element method for the Stokes equations

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Author(s)Ye, Xiu
Author(s)Zhang, Shangyou
Date Accessioned2021-12-22T20:41:11Z
Date Available2021-12-22T20:41:11Z
Publication Date2021-04-08
DescriptionThis article was originally published in Advances in Computational Mathematics. The version of record is available at: https://doi.org/10.1007/s10444-021-09856-9en_US
AbstractIn 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
SponsorXiu Ye was supported in part by the National Science Foundation Grant DMS-1620016.en_US
CitationYe, 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/s10444-021-09856-9en_US
ISSN1572-9044
URLhttps://udspace.udel.edu/handle/19716/29914
Languageen_USen_US
PublisherAdvances in Computational Mathematicsen_US
KeywordsWeak gradienten_US
KeywordsFinite element methodsen_US
KeywordsThe Stokes equationsen_US
KeywordsPressure-robusten_US
TitleA stabilizer-free pressure-robust finite element method for the Stokes equationsen_US
TypeArticleen_US
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