Augmenting the grad-div stabilization for Taylor–Hood finite elements with a vorticity stabilization
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Volker John
Abstract
The least squares vorticity stabilization (LSVS), proposed in N. Ahmed, G. R. Barrenechea, E. Burman, J. Guzmán, A. Linke, and C. Merdon (“A pressure-robust discretization of Oseen’s equation using stabilization in the vorticity equation,” SIAM J. Numer. Anal., vol. 59, no. 5, pp. 2746–2774, 2021) for the Scott–Vogelius finite element discretization of the Oseen equations, is studied as an augmentation of the popular grad-div stabilized Taylor–Hood pair of spaces. An error analysis is presented which exploits the situation that the velocity spaces of Scott–Vogelius and Taylor–Hood are identical. Convection-robust error bounds are derived under the assumption that the Scott–Vogelius discretization is well posed on the considered grid. Numerical studies support the analytic results and they show that the LSVS-grad-div method might lead to notable error reductions compared with the standard grad-div method.
Funding source: The Berlin Mathematical School Phase I / Phase II scholarships
Acknowledgments
The work of Marwa Zainelabdeen was supported by the Berlin Mathematical School.
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Research ethics: Not applicable.
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Informed consent: Not applicable.
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Author contributions: All authors have contributed to the numerical analysis and the preparation of the manuscript. The authors Ch. Merdon and M. Zainelabdeen performed the numerical simulations. All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Use of Large Language Models, AI and Machine Learning Tools: None declared.
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Conflict of interest: The author states no conflict of interest.
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Research funding: The work of Marwa Zainelabdeen was supported by the Berlin Mathematical School Phase I / Phase II scholarships.
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Data availability: Not applicable.
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Stabilized weighted reduced order methods for parametrized advection-dominated optimal control problems governed by partial differential equations with random inputs
- Augmenting the grad-div stabilization for Taylor–Hood finite elements with a vorticity stabilization
- Obtaining higher-order Galerkin accuracy when the boundary is polygonally approximated
- Optimal evaluation of symmetry-adapted n-correlations via recursive contraction of sparse symmetric tensors
Articles in the same Issue
- Frontmatter
- Stabilized weighted reduced order methods for parametrized advection-dominated optimal control problems governed by partial differential equations with random inputs
- Augmenting the grad-div stabilization for Taylor–Hood finite elements with a vorticity stabilization
- Obtaining higher-order Galerkin accuracy when the boundary is polygonally approximated
- Optimal evaluation of symmetry-adapted n-correlations via recursive contraction of sparse symmetric tensors
