no. 5
An embedded discontinuous Galerkin method for the Oseen equations
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 5, pp. 2349-2364

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.

DOI : 10.1051/m2an/2021059
Classification : 65N12, 65N22, 65N30, 76D07
Keywords: Reynolds-robust, quasi-optimal, embedded discontinuous Galerkin method, Oseen equations 
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     title = {An embedded discontinuous {Galerkin} method for the {Oseen} equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {2349--2364},
     year = {2021},
     publisher = {EDP-Sciences},
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Han, Yongbin; Hou, Yanren. An embedded discontinuous Galerkin method for the Oseen equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 5, pp. 2349-2364. doi: 10.1051/m2an/2021059

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