{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T07:06:23Z","timestamp":1776755183216,"version":"3.51.2"},"reference-count":39,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2017,2,1]],"date-time":"2017-02-01T00:00:00Z","timestamp":1485907200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["14-31-00024"],"award-info":[{"award-number":["14-31-00024"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[2017,5]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>The paper studies numerical properties of LU and incomplete LU factorizations applied to the discrete linearized incompressible Navier\u2013Stokes problem also known as the Oseen problem. A commonly used stabilized Petrov\u2013Galerkin finite element method for the Oseen problem leads to the system of algebraic equations having a 2\u00a0\u00d7\u00a02\u2010block structure. While enforcing better stability of the finite element solution, the Petrov\u2013Galerkin method perturbs the saddle\u2010point structure of the matrix and may lead to less favorable algebraic properties of the system. The paper analyzes the stability of the LU factorization. This analysis quantifies the effect of the streamline upwind Petrov\u2013Galerkin stabilization in terms of the perturbation made to a nonstabilized system. The further analysis shows how the perturbation depends on the particular finite element method, the choice of stabilization parameters, and flow problem parameters. The analysis of LU factorization and its stability helps to understand the properties of threshold ILU factorization preconditioners for the system. Numerical experiments for a model problem of blood flow in a coronary artery illustrate the performance of the threshold ILU factorization as a preconditioner. The dependence of the preconditioner properties on the stabilization parameters of the finite element method is also studied numerically.<\/jats:p>","DOI":"10.1002\/nla.2085","type":"journal-article","created":{"date-parts":[[2017,2,1]],"date-time":"2017-02-01T07:05:08Z","timestamp":1485932708000},"source":"Crossref","is-referenced-by-count":7,"title":["LU factorizations and ILU preconditioning for stabilized discretizations of incompressible Navier\u2013Stokes equations"],"prefix":"10.1002","volume":"24","author":[{"given":"Igor","family":"Konshin","sequence":"first","affiliation":[{"name":"Institute of Numerical Mathematics and Dorodnicyn Computing Centre FRC IC Russian Academy of Sciences  Moscow Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maxim","family":"Olshanskii","sequence":"additional","affiliation":[{"name":"Department of Mathematics University of Houston  Houston TX 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