Volume 55, Number 5, September-October 2021
|Page(s)||2349 - 2364|
|Published online||21 October 2021|
An embedded discontinuous Galerkin method for the Oseen equations
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, P.R. China
* Corresponding author: firstname.lastname@example.org
Accepted: 20 September 2021
In this paper, the a priori error estimates of an embedded discontinuous Galerkin method for the Oseen equations are presented. It is proved that the velocity error in the L2(Ω) norm, has an optimal error bound with convergence order k + 1, where the constants are dependent on the Reynolds number (or ν−1), in the diffusion-dominated regime, and in the convection-dominated regime, it has a Reynolds-robust error bound with quasi-optimal convergence order k + 1/2. Here, k is the polynomial order of the velocity space. In addition, we also prove an optimal error estimate for the pressure. Finally, we carry out some numerical experiments to corroborate our analytical results.
Mathematics Subject Classification: 65N12 / 65N22 / 65N30 / 76D07
Key words: Reynolds-robust / quasi-optimal / embedded discontinuous Galerkin method / Oseen equations
© The authors. Published by EDP Sciences, SMAI 2021
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