Local projection stabilization with discontinuous Galerkin method in time applied to convection dominated problems in time-dependent domains

2019 ◽  
Vol 60 (2) ◽  
pp. 481-507
Author(s):  
Shweta Srivastava ◽  
Sashikumaar Ganesan
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Time Dependent ◽  
Local Projection ◽  
Local Projection Stabilization ◽  
Convection Dominated

scholarly journals An embedded discontinuous Galerkin method for the Oseen equations

2021 ◽  
Author(s):  
Yongbin Han ◽  
Yanren Hou
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Error Bound ◽  
Discontinuous Galerkin Method ◽  
Convergence Order ◽  
Optimal Error Estimate ◽  
Optimal Error ◽  
Oseen Equations ◽  
Optimal Error Bound ◽  
Convection Dominated

In this paper, the a prior 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.

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