Energy norma posteriorierror estimation for divergence‐free discontinuous Galerkin approximations of the Navier–Stokes equations

2008 ◽  
Vol 57 (9) ◽  
pp. 1093-1113 ◽  
Author(s):  
Guido Kanschat ◽  
Dominik Schötzau
Keyword(s):  
Discontinuous Galerkin ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Galerkin Approximations ◽  
Divergence Free

Exponential convergence of mixed hp-DGFEM for the incompressible Navier–Stokes equations in ℝ2

2020 ◽  
Author(s):  
Dominik Schötzau ◽  
Carlo Marcati ◽  
Christoph Schwab
Keyword(s):  
Discontinuous Galerkin ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Rates Of Convergence ◽  
Navier Stokes ◽  
Small Data ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Hp Spaces ◽  
Galerkin Approximations

Abstract In a polygon $\varOmega \subset \mathbb{R}^2$ we consider mixed $hp$-discontinuous Galerkin approximations of the stationary, incompressible Navier–Stokes equations, subject to no-slip boundary conditions. We use geometrically corner-refined meshes and $hp$ spaces with linearly increasing polynomial degrees. Based on recent results on analytic regularity of velocity field and pressure of Leray solutions in $\varOmega$, we prove exponential rates of convergence of the mixed $hp$-discontinuous Galerkin finite element method, with respect to the number of degrees of freedom, for small data which is piecewise analytic.

scholarly journals Discontinuous Galerkin approximations of the Stokes and Navier-Stokes equations

2010 ◽  
Vol 79 (272) ◽  
pp. 2135-2135 ◽  
Author(s):  
Konstantinos Chrysafinos ◽  
Noel J. Walkington
Keyword(s):  
Discontinuous Galerkin ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Galerkin Approximations

scholarly journals A Note on Discontinuous Galerkin Divergence-free Solutions of the Navier–Stokes Equations

2006 ◽  
Vol 31 (1-2) ◽  
pp. 61-73 ◽  
Author(s):  
Bernardo Cockburn ◽  
Guido Kanschat ◽  
Dominik Schötzau
Keyword(s):  
Discontinuous Galerkin ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Divergence Free
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