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Higher-order discontinuous Galerkin time discretizations the evolutionary Navier--Stokes equations (1910.12599v1)
Published 28 Oct 2019 in math.NA and cs.NA
Abstract: 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.