Publisher DOI: 10.1002/num.21752
Title: Efficient linear solvers for incompressible flow simulations using Scott-Vogelius finite elements
Language: English
Authors: Cousins, Benjamin R. 
Le Borne, Sabine  
Linke, Alexander 
Rebholz, Leo G. 
Wang, Zhen 
Keywords: augmented lagrangian preconditioning; H-Lu; linear solvers; scott-Vogelius elements; static condensation
Issue Date: 5-Dec-2012
Publisher: Wiley
Source: Numerical Methods for Partial Differential Equations 4 (29): 1217-1237 (2013)
Abstract (english): 
Recent research has shown that in some practically relevant situations like multiphysics flows (Galvin et al., Comput Methods Appl Mech Eng, to appear) divergence-free mixed finite elements may have a significantly smaller discretization error than standard nondivergence-free mixed finite elements. To judge the overall performance of divergence-free mixed finite elements, we investigate linear solvers for the saddle point linear systems arising in ((Pk)d,Pk-1disc) Scott-Vogelius finite element implementations of the incompressible Navier-Stokes equations. We investigate both direct and iterative solver methods. Due to discontinuous pressure elements in the case of Scott-Vogelius (SV) elements, considerably more solver strategies seem to deliver promising results than in the case of standard mixed finite elements such as Taylor-Hood elements. For direct methods, we extend recent preliminary work using sparse banded solvers on the penalty method formulation to finer meshes and discuss extensions. For iterative methods, we test augmented Lagrangian and ℋ -LU preconditioners with GMRES, on both full and statically condensed systems. Several numerical experiments are provided that show these classes of solvers are well suited for use with SV elements and could deliver an interesting overall performance in several applications.
ISSN: 1098-2426
Journal: Numerical methods for partial differential equations 
Institute: Mathematik E-10 
Document Type: Article
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