Abstract
We introduce two new lowest order methods, a mixed method, and a hybrid discontinuous Galerkin method, for the approximation of incompressible flows. Both methods use divergence-conforming linear Brezzi–Douglas–Marini space for approximating the velocity and the lowest order Raviart–Thomas space for approximating the vorticity. Our methods are based on the physically correct viscous stress tensor of the fluid, involving the symmetric gradient of velocity (rather than the gradient), provide exactly divergence-free discrete velocity solutions, and optimal error estimates that are also pressure robust. We explain how the methods are constructed using the minimal number of coupling degrees of freedom per facet. The stability analysis of both methods are based on a Korn-like inequality for vector finite elements with continuous normal component. Numerical examples illustrate the theoretical findings and offer comparisons of condition numbers between the two new methods.
Original language | English |
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Article number | 91 |
Number of pages | 25 |
Journal | Journal of scientific computing |
Volume | 95 |
Issue number | 3 |
Early online date | 11 May 2023 |
DOIs | |
Publication status | Published - Jun 2023 |
Keywords
- UT-Hybrid-D
- Hybrid discontinuous Galerkin methods
- Incompressible Stokes equations
- Mixed finite elements
- Pressure-robustness
- Discrete Korn inequality
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Computational results and python files for the work "Divergence-conforming velocity and vorticity approximations for incompressible fluids obtained with minimal facet coupling"
Lederer, P. (Creator), Kogler, L. (Creator), Gopalakrishnan, J. (Creator) & Schöberl, J. (Creator), Zenodo, 24 Mar 2023
DOI: 10.5281/zenodo.7767775, https://zenodo.org/record/7767775
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