{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:42:04Z","timestamp":1787330524940,"version":"build-2736575974"},"reference-count":47,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010661","name":"Horizon 2020 Framework Programme","doi-asserted-by":"publisher","award":["705402"],"award-info":[{"award-number":["705402"]}],"id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002924","name":"Federaci\u00f3n Espa\u00f1ola de Enfermedades Raras","doi-asserted-by":"publisher","award":["MTM2013-40842-P"],"award-info":[{"award-number":["MTM2013-40842-P"]}],"id":[{"id":"10.13039\/501100002924","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>The multigrid solution of coupled porous media and Stokes flow problems is considered. The Darcy equation as the saturated porous medium model is coupled to the Stokes equations by means of appropriate interface conditions. We focus on an efficient multigrid solution technique for the coupled problem, which is discretized by finite volumes on staggered grids, giving rise to a saddle point linear system. Special treatment is required regarding the discretization at the interface. An Uzawa smoother is employed in multigrid, which is a decoupled procedure based on symmetric Gauss--Seidel smoothing for velocity components and a simple Richardson iteration for the pressure field. Since a relaxation parameter is part of a Richardson iteration, local Fourier analysis is applied to determine the optimal parameters. Highly satisfactory multigrid convergence is reported, and, moreover, the algorithm performs very well for small values of the hydraulic conductivity and fluid viscosity, which are relevant for applications.<\/jats:p>","DOI":"10.1137\/16m1076514","type":"journal-article","created":{"date-parts":[[2017,10,26]],"date-time":"2017-10-26T16:24:40Z","timestamp":1509035080000},"page":"S633-S661","source":"Crossref","is-referenced-by-count":24,"title":["Uzawa Smoother in Multigrid for the Coupled Porous Medium and Stokes Flow System"],"prefix":"10.1137","volume":"39","author":[{"given":"Peiyao","family":"Luo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Carmen","family":"Rodrigo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francisco J.","family":"Gaspar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cornelis W.","family":"Oosterlee","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,10,26]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/151006135"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2010.07.008"},{"key":"atypb3","volume-title":"Iterative Solution Methods","author":"Axelsson O.","year":"1996"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492904000212"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(96)00059-1"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1977-0431719-X"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1137\/0731087"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-546050-7.50008-3"},{"key":"atypb9","volume-title":"Classics Appl. Math. 67","author":"Brandt A.","year":"2011"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2009.07.029"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1007\/s10596-014-9418-y"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/080731542"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.4310\/CMS.2010.v8.n1.a2"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/080740556"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1137\/15M1032156"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/j.advwatres.2009.10.012"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(02)00125-3"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/s00791-003-0113-0"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.5209\/rev_REMA.2009.v22.n2.16263"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/06065091X"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/s00791-007-0061-1"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1002\/nla.372"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1137\/130920630"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1016\/j.cej.2008.10.012"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1063\/1.1761178"},{"key":"atypb26","volume-title":"Bachelor's thesis","author":"Hoffmann M.","year":"2013"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1137\/S003613999833678X"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1002\/1097-0363(20000630)33:4<453::AID-FLD15>3.0.CO;2-0"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100047642"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1615\/Int.J.UncertaintyQuantification.2016018677"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1002\/nla.561"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901392766"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7225(75)90054-3"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2074"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-663-14245-4_8"},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-013-9700-5"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2007.11.014"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7930(88)90024-2"},{"key":"atypb39","volume-title":"Numer. Math. Sci. Comput.","author":"Quarteroni A.","year":"1999"},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142903427640"},{"key":"atypb41","doi-asserted-by":"publisher","DOI":"10.1007\/s10596-015-9469-8"},{"key":"atypb42","doi-asserted-by":"publisher","DOI":"10.1002\/sapm197150293"},{"key":"atypb43","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-10064-7"},{"key":"atypb44","volume-title":"Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations","author":"Smith B.","year":"2004"},{"key":"atypb45","volume-title":"Multigrid","author":"Trottenberg U.","year":"2001"},{"key":"atypb46","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(86)90008-2"},{"key":"atypb47","volume-title":"Practical Fourier Analysis for Multigrid Methods","author":"Wienands R.","year":"2005"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1076514","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:10:41Z","timestamp":1787328641000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1076514"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1]]},"references-count":47,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["10.1137\/16M1076514"],"URL":"https:\/\/doi.org\/10.1137\/16m1076514","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1]]}}}