Barrenechea, Gabriel R;
Burman, Erik;
Cáceres, Ernesto;
Guzman, Johnny;
(2024)
Continuous interior penalty stabilization for divergence-free finite element methods.
IMA Journal of Numerical Analysis
, 44
(2)
pp. 980-1002.
10.1093/imanum/drad030.
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Abstract
In this paper, we propose, analyze and test numerically a pressure-robust stabilized finite element for a linearized problem in incompressible fluid mechanics, namely, the steady Oseen equation with low viscosity. Stabilization terms are defined by jumps of different combinations of derivatives for the convective term over the element faces of the triangulation of the domain. With the help of these stabilizing terms, and the fact the finite element space is assumed to provide a point-wise divergence-free velocity, an $\mathcal O\big(h^{k+\frac 12}\big)$ error estimate in the $L^2$-norm is proved for the method (in the convection-dominated regime), and optimal order estimates in the remaining norms of the error. Numerical results supporting the theoretical findings are provided.
| Type: | Article |
|---|---|
| Title: | Continuous interior penalty stabilization for divergence-free finite element methods |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/imanum/drad030 |
| Publisher version: | https://doi.org/10.1093/imanum/drad030 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10172786 |
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