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

2019/10/28 by Naveed Ahmed, Ahmed, Naveed, Gunar Matthies +1
Engineering · Physics and Astronomy · #65M12 #65M15 #65M60 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1910.12599

openalex publication_date 2019/10/28 · openalex created_date 2022/07/24 · openalex updated_date 2026/07/28

Abstract

Discontinuous Galerkin methods of higher order are applied as temporal\ndiscretizations for the transient Navier--Stokes equations. The spatial\ndiscretization based on inf-sup stable pairs of finite element spaces is\nstabilised using a one-level local projection stabilisation method. Optimal\nerror bounds for the velocity with constants independent of the viscosity\nparameter are obtained for the semi-discrete case. For the fully discrete case,\nerror estimates for both velocity and pressure are given. Numerical results\nsupport the theoretical predictions.\n

Related

• Optimal Error Estimates of a Discontinuous Galerkin Method for the Navier-Stokes Equations
• Fully and semi-implicit robust space-time DG methods for the incompressible Navier-Stokes equations
• Higher order Galerkin-collocation time discretization with Nitsche's\n method for the Navier-Stokes equations
• Improved a priori error estimates for a discontinuous Galerkin pressure correction scheme for the Navier-Stokes equations
• A Stable and High-Order Accurate Discontinuous Galerkin Based Splitting\n Method for the Incompressible Navier-Stokes Equations