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

10/28/2019

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by   Naveed Ahmed, et al.

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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 stabilised using a one-level local projection stabilisation method. Optimal error bounds for the velocity with constants independent of the viscosity parameter are obtained for the semi-discrete case. For the fully discrete case, error estimates for both velocity and pressure are given. Numerical results support the theoretical predictions.