An embedded discontinuous Galerkin method for the Oseen equations

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 L 2 (Ω) norm, has an optimal error bound with convergence order k  + 1, where the constants are dependent on the Reynolds number...

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Bibliographic Details
Published in:ESAIM. Mathematical modelling and numerical analysis 2021-09, Vol.55 (5), p.2349-2364
Main Authors: Han, Yongbin, Hou, Yanren
Format: Article
Language:English
Subjects:
Convergence
Fluid flow
Galerkin method
Mathematical analysis
Polynomials
Reynolds number
Robustness (mathematics)
Velocity errors
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Summary: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 L 2 (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.
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an/2021059