Higher-order discontinuous Galerkin time stepping and local projection stabilization techniques for the transient Stokes problem

2017 ◽  
Vol 313 ◽  
pp. 28-52 ◽  
Author(s):  
Naveed Ahmed ◽  
Simon Becher ◽  
Gunar Matthies
Keyword(s):  
Discontinuous Galerkin ◽  
Stokes Problem ◽  
Higher Order ◽  
Local Projection ◽  
Time Stepping ◽  
Local Projection Stabilization

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 Local projection stabilization of equal order interpolation applied to the Stokes problem

2008 ◽  
Vol 77 (264) ◽  
pp. 2039-2060 ◽  
Author(s):  
Sashikumaar Ganesan ◽  
Gunar Matthies ◽  
Lutz Tobiska
Keyword(s):  
Stokes Problem ◽  
Local Projection ◽  
Local Projection Stabilization

scholarly journals Local Projection Stabilization Method for Incompressible Flow Problems

2012 ◽  
Vol 17 (2) ◽  
pp. 187
Author(s):  
A.M. Essefi ◽  
K. Nafa
Keyword(s):  
Stokes Problem ◽  
Rates Of Convergence ◽  
Stabilization Method ◽  
Local Projection ◽  
Numerical Examples ◽  
Flow Problems ◽  
Local Projection Stabilization ◽  
Optimal Rates Of Convergence ◽  
Stability And Accuracy ◽  
Methods Numerical

We analyze Local Projection Stabilization (LPS) methods for the solution of Stokes problem using equal order finite elements. We investigate their convergence, stability and accuracy properties. The resulting stabilized method is shown to lead to optimal rates of convergence for both velocity and pressure approximations. We distinguish two classes of LPS methods: one-level and two-level methods. Numerical examples using bilinear interpolations are presented to validate the analysis and assess the accuracy of both approaches.  

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