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Title: Efficient linear solvers for incompressible flow simulations using Scott-Vogelius finite elements
Authors: Cousins, BenjaminLe Borne, SabineLinke, AlexanderRebholz, Leo G.Wang, Zhen
Issue Date: 2013
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 1821, ISSN 0946 – 8633
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: Recent research has shown that in some practically relevant situations like multi-physics flows [11] divergence-free mixed finite elements may have a significantly smaller discretization error than standard nondivergence-free mixed finite elements. In order 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; Pdisc k-1 )) 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 elements, considerably more solver strategies seem to deliver promising results than in the case of standard mixed finite elements like 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
Keywords: Scott-Vogelius elements; linear solvers; static condensation; augmented Lagrangian preconditioning; H-LU; inkompressible Strömung; Finite-Elemente-Methode
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
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