Higher-order discontinuous Galerkin time discretizations for the evolutionary Navier-Stokes equations

Discontinuous Galerkin methods of higher order are applied as temporal discretizations for the transient Navier-Stokes equations. The spatial discretization based on inf-sup stable pairs of finite element spaces is stabilized using a one-level local projection stabilization method. Optimal error bounds for the velocity with constants independent of the viscosity parameter are obtained for both the semidiscrete case and the fully discrete case. Numerical results support the theoretical predictions.

Automated summary

The paper utilizes higher-order discontinuous Galerkin methods for temporal discretizations of the transient Navier-Stokes equations, and stabilizes the spatial discretization using inf-sup stable pairs of finite element spaces with a one-level local projection stabilization method. Optimal error bounds for the velocity with viscosity parameter-independent constants are obtained for both the semidiscrete and fully discrete cases, and numerical results confirm the theoretical predictions.