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Inf–sup stabilized Scott–Vogelius pairs on general shape-regular simplicial grids by Raviart–Thomas enrichment.
- Source :
-
Mathematical Models & Methods in Applied Sciences . May2024, Vol. 34 Issue 5, p919-949. 31p. - Publication Year :
- 2024
-
Abstract
- This paper considers the discretization of the Stokes equations with Scott–Vogelius pairs of finite element spaces on arbitrary shape-regular simplicial grids. A novel way of stabilizing these pairs with respect to the discrete inf–sup condition is proposed and analyzed. The key idea consists in enriching the continuous polynomials of order k of the Scott–Vogelius velocity space with appropriately chosen and explicitly given Raviart–Thomas bubbles. This approach is inspired by [X. Li and H. Rui, A low-order divergence-free H (div) -conforming finite element method for Stokes flows, IMA J. Numer. Anal.42 (2022) 3711–3734], where the case k = 1 was studied. The proposed method is pressure-robust, with optimally converging H 1 -conforming velocity and a small H (div) -conforming correction rendering the full velocity divergence-free. For k ≥ d , with d being the dimension, the method is parameter-free. Furthermore, it is shown that the additional degrees of freedom for the Raviart–Thomas enrichment and also all non-constant pressure degrees of freedom can be eliminated, effectively leading to a pressure-robust, inf–sup stable, optimally convergent P k × P 0 scheme. Aspects of the implementation are discussed and numerical studies confirm the analytic results. [ABSTRACT FROM AUTHOR]
- Subjects :
- *STOKES equations
*STOKES flow
*DEGREES of freedom
*FINITE element method
Subjects
Details
- Language :
- English
- ISSN :
- 02182025
- Volume :
- 34
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Mathematical Models & Methods in Applied Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 176467478
- Full Text :
- https://doi.org/10.1142/S0218202524500180