{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:30:23Z","timestamp":1787329823294,"version":"build-2736575974"},"reference-count":21,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[1995,9]]},"abstract":"<jats:p>The least-squares mixed finite element technique developed in Part I is applied to non-selfadjoint second-order elliptic problems. This approach leads to a symmetric positive definite bilinear form which is coercive uniformly in the discretization parameter. In this paper we consider an approximate block-factorization technique recently proposed by Chan and Vassilevski in [A framework for block-ILU factorization using block size reduction, Math. Comp., 64 (1995), pp. 129\u2013156] and which is well defined for positive definite block-tridiagonal matrices. The method is analyzed and supported with extensive numerical experiments.<\/jats:p>","DOI":"10.1137\/0916065","type":"journal-article","created":{"date-parts":[[2005,3,1]],"date-time":"2005-03-01T03:42:54Z","timestamp":1109648574000},"page":"1126-1136","source":"Crossref","is-referenced-by-count":21,"title":["Least-Squares Mixed Finite Element Methods for Non-Selfadjoint Elliptic Problems: II. Performance of Block-ILU Factorization Methods"],"prefix":"10.1137","volume":"16","author":[{"given":"G. F.","family":"Carey","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A. I.","family":"Pehlivanov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P. S.","family":"Vassilevski","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,13]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(86)90159-X"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01436561"},{"key":"R3","volume-title":"Multigrid methods","author":"Bramble J. H.","year":"1992"},{"key":"R4","first-page":"129","volume":"8","author":"Brezzi F.","year":"1974","journal-title":"Rev. Fran\u00e7aise Automat. Informat. Recherche Op\u00e9rationnelle S\u00e9r. Rouge"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-3172-1"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202593000151"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/0914065"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1995-1257575-9"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/0906018"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/0731086"},{"key":"R11","unstructured":"R. E. Ewing, J. E. Pasciak, P. S. Vassilevski,  Hybrid hierarchical multilevel methods for mixed finite element systems with penalty,  1991, EORI, University of Wyoming, preprint"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(88)90168-5"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61623-5"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(84)90022-7"},{"key":"R15","volume-title":"The mathematical theory of viscous incompressible flow","author":"Ladyzhenskaya O. A.","year":"1969"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1007\/BF01400312"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1994280504991"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050179"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.7146\/math.scand.a-11983"},{"key":"R20","unstructured":"P. S. Vassilevski,  Iterative solution of finite element elliptic equations, CAM Report, 92-41, Department of Mathematics, University of California, Los Angeles, CA,  1992"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1007\/BF01385872"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/0916065","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:35:31Z","timestamp":1787326531000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/0916065"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,9]]},"references-count":21,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1995,9]]}},"alternative-id":["10.1137\/0916065"],"URL":"https:\/\/doi.org\/10.1137\/0916065","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,9]]}}}