scholarly journals Optimal error bounds for two-grid schemes applied to the Navier–Stokes equations

2012 ◽  
Vol 218 (13) ◽  
pp. 7034-7051 ◽  
Author(s):  
Javier de Frutos ◽  
Bosco García-Archilla ◽  
Julia Novo
Keyword(s):  
Error Bounds ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Optimal Error ◽  
Navier Stokes Equations

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

2020 ◽  
Author(s):  
Naveed Ahmed ◽  
Gunar Matthies
Keyword(s):  
Discontinuous Galerkin ◽  
Stokes Equations ◽  
Higher Order ◽  
Navier Stokes ◽  
Optimal Error ◽  
Navier Stokes Equations ◽  
Fully Discrete ◽  
Local Projection Stabilization ◽  
Theoretical Predictions ◽  
Stable Pairs

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 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.

scholarly journals Resolution and implementation of the nonstationary vorticity velocity pressure formulation of the Navier–Stokes equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mohamed Abdelwahed ◽  
Ebtisam Alharbi ◽  
Nejmeddine Chorfi ◽  
Henda Ouertani
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Optimal Error Estimate ◽  
Optimal Error ◽  
Navier Stokes Equations ◽  
Implicit Euler Scheme ◽  
Numerical Tests ◽  
Pressure Formulation ◽  
Velocity Pressure ◽  
Spectral Discretization

Abstract This paper deals with the iterative algorithm and the implementation of the spectral discretization of time-dependent Navier–Stokes equations in dimensions two and three. We present a variational formulation, which includes three independent unknowns: the vorticity, velocity, and pressure. In dimension two, we establish an optimal error estimate for the three unknowns. The discretization is deduced from the implicit Euler scheme in time and spectral methods in space. We present a matrix linear system and some numerical tests, which are in perfect concordance with the analysis.

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