{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T07:39:26Z","timestamp":1787384366770,"version":"build-2736575974"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[1999,1]]},"abstract":"<jats:p>We propose an abstract two-grid algorithm with convergence independent of the coarse-space size. The abstract algorithm is applied to problems of three-dimensional linear elasticity discretized on unstructured meshes. With no regularity assumptions we prove uniform convergence with respect to coarse-space size, domain, essential boundary conditions, and jumps in Young modulus. Numerical experiments confirm the theory and show that the method works well even if some assumptions of the theory are violated.<\/jats:p>","DOI":"10.1137\/s1064827596297112","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"900-923","source":"Crossref","is-referenced-by-count":31,"title":["Two-grid Method for Linear Elasticity on Unstructured Meshes"],"prefix":"10.1137","volume":"21","author":[{"given":"Petr","family":"Vanek","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marian","family":"Brezina","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Radek","family":"Tezaur","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,2,17]]},"reference":[{"key":"R1","unstructured":"R. A. Adams,\n                      Sobolev Spaces\n                      , Academic Press, New York, 1975."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(78)90026-9"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01406510"},{"key":"R4","unstructured":"J. H. Bramble,\n                      Multigrid Methods\n                      , PitmanRes. Notes Math. Sci. Ser., 294, Longman Scientific & Technical, Harlow, England, 1993."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1986-0842125-3"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-98-00879-5"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1991-1079008-4"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/0096-3003(86)90095-0"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4338-8"},{"key":"R10","unstructured":"M. Brezina,\n                      Robust Iterative Solvers on Unstructured Meshes\n                      , Ph.D. thesis, University of Colorado at Denver, Denver, CO, 1997."},{"key":"R11","unstructured":"T. F. Chan, S. Margenov, and P. Vassilevski,\n                      Performance of block\u2010ILU factorization preconditioners based on block\u2010size reduction for 2D elasticity systems\n                      , Tech. report 94\u201033, Department of Math., UCLA, Los Angeles, CA, 1994, CAM report."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1007\/BF01602271"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1137\/0731086"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1955-0069585-4"},{"key":"R15","first-page":"641","volume":"10","author":"Kondratiev V.","year":"1990","journal-title":"Rend. Mat. Appl. (7)"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1506(199607\/08)3:4<255::AID-NLA77>3.0.CO;2-2"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.1640090307"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1007\/BF02165096"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.21136\/AM.1992.104509"},{"key":"R20","unstructured":"P. Van\u011bk and J. K\u0159\u00ed\u017ekov\u00e1,\n                      Two\u2013Level Method on Unstructured Meshes with Convergence Rate Independent of the Coarse\u2010Space Size\n                      , Tech. Report 35, Center Computational Mathematics, 1995."},{"key":"R21","unstructured":"P. Van\u011bk, J. Mandel, and M. Brezina,\n                      Algebraic Multigrid on Unstructured Meshes\n                      , UCD\/CCM Report 34, Center for Computational Mathematics, University of Colorado at Denver, Denver, CO, 1994."},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1007\/BF02238511"},{"key":"R23","unstructured":"P. Van\u011bk, J. Mandel, and M. Brezina,\n                      Solving a Two\u2010Dimensional Helmholtz Problem Using Algebraic Multigrid\n                      , UCD\/CCM Report 110, Center for Computational Mathematics, University of Colorado at Denver, Denver, CO, 1997."},{"key":"R24","unstructured":"P. Van\u011bk, R. Tezaur, M. Brezina, and J. K\u011b\u00ed\u017ekov\u00e1,\n                      Two\u2010level method with coarse space size independent convergence\n                      , in Domain Decomposition Methods in Sciences and Engineering, R. Glowinski, J. P\u00e9riaux, Z. Shi, and O. Widlund, eds., John Wiley & Sons, New York, 1997."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827596297112","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:37:43Z","timestamp":1787333863000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827596297112"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,1]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1999,1]]}},"alternative-id":["10.1137\/S1064827596297112"],"URL":"https:\/\/doi.org\/10.1137\/s1064827596297112","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,1]]}}}