scholarly journals Discontinuous Galerkin methods for the Stokes equations using divergence‐free approximations

2008 ◽  
Vol 57 (9) ◽  
pp. 1071-1092 ◽  
Author(s):  
A. Montlaur ◽  
S. Fernandez‐Mendez ◽  
A. Huerta
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Stokes Equations ◽  
Galerkin Methods ◽  
Divergence Free

scholarly journals Hybrid Discontinuous Galerkin methods with relaxed H(div)-conformity for incompressible flows. Part II

2019 ◽  
Vol 53 (2) ◽  
pp. 503-522 ◽  
Author(s):  
Philip L. Lederer ◽  
Christoph Lehrenfeld ◽  
Joachim Schöberl
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Integration Scheme ◽  
Galerkin Methods ◽  
Robust Analysis ◽  
Reconstruction Operator ◽  
The Impact

The present work is the second part of a pair of papers, considering Hybrid Discontinuous Galerkin methods with relaxed H(div)-conformity. The first part mainly dealt with presenting a robust analysis with respect to the mesh size h and the introduction of a reconstruction operator to restore divergence-conformity and pressure robustness (pressure independent velocity error estimates) using a modified force discretization. The aim of this part is the presentation of a high order polynomial robust analysis for the relaxed H(div)-conforming Hybrid Discontinuous Galerkin discretization of the two dimensional Stokes problem. It is based on the recently proven polynomial robust LBB-condition for BDM elements, Lederer and Schöberl (IMA J. Numer. Anal. (2017)) and is derived by a direct approach instead of using a best approximation Céa like result. We further treat the impact of the reconstruction operator on the hp analysis and present a numerical investigation considering polynomial robustness. We conclude the paper presenting an efficient operator splitting time integration scheme for the Navier–Stokes equations which is based on the methods recently presented in Lehrenfeld and Schöberl (Comp. Methods Appl. Mech. Eng. 307 (2016) 339–361) and includes the ideas of the reconstruction operator.

scholarly journals Multigrid methods for Hdiv-conforming discontinuous Galerkin methods for the Stokes equations

2015 ◽  
Vol 23 (1) ◽  
Author(s):  
Guido Kanschat ◽  
Youli Mao
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Multigrid Method ◽  
Stokes System ◽  
Stokes Equations ◽  
Multigrid Methods ◽  
Galerkin Methods

AbstractA multigrid method for the Stokes system discretized with an H

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