Publisher DOI: 10.1016/j.cma.2014.02.021
Title: Error analysis and iterative solvers for Navier–Stokes projection methods with standard and sparse grad-div stabilization
Language: English
Authors: Bowers, Abigail L. 
Le Borne, Sabine  
Rebholz, Leo G. 
Keywords: Navier–Stokes equations;Projection methods;Sparse grad-div stabilization;Mass conservation;Iterative solvers
Issue Date: 15-Jun-2014
Publisher: Elsevier
Source: Computer Methods in Applied Mechanics and Engineering (275): 1-19 (2014)
Abstract (english): 
This paper shows that use of a recently introduced sparse grad-div stabilization can increase the accuracy of projection methods for solving the Navier–Stokes equations. Sparse grad-div stabilization has recently been introduced as an alternative to standard grad-div stabilization which has a sparser matrix representation. For both sparse and standard grad-div stabilized projection methods, we prove error estimates and provide numerical experiments which reveal that both stabilizations can cause a significant decrease in the error. We then compare iterative solvers for the linear systems of equations arising from the use of both of the stabilizations. A theoretical analysis of a simplified model problem as well as numerical tests show that iterative solvers perform better for systems arising from sparse grad-div compared to standard grad-div stabilized systems.
ISSN: 0045-7825
Institute: Mathematik E-10 
Document Type: Article
Journal: Computer methods in applied mechanics and engineering 
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