{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T18:34:23Z","timestamp":1777142063135,"version":"3.51.4"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T00:00:00Z","timestamp":1777075200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T00:00:00Z","timestamp":1777075200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["No. 12171071"],"award-info":[{"award-number":["No. 12171071"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["No. 12431015"],"award-info":[{"award-number":["No. 12431015"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"the Natural Science Foundation of Sichuan Province","award":["2023NSFSC0055"],"award-info":[{"award-number":["2023NSFSC0055"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1007\/s10915-026-03295-8","type":"journal-article","created":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T17:43:07Z","timestamp":1777138987000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Domain Decomposition Methods for the Coupled Stokes Flows under the Signorini-Type Interface Condition"],"prefix":"10.1007","volume":"107","author":[{"given":"Yangyang","family":"Song","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8712-1934","authenticated-orcid":false,"given":"Ping","family":"Zeng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guanyu","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,4,25]]},"reference":[{"key":"3295_CR1","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/BF01406510","volume":"55","author":"C B\u00f6rgers","year":"1989","unstructured":"B\u00f6rgers, C.: The Neumann-Dirichlet domain decomposition method with inexact solvers on the subdomains. Numer. Math. 55, 123\u2013136 (1989)","journal-title":"Numer. Math."},{"key":"3295_CR2","doi-asserted-by":"crossref","unstructured":"Brenner, S.C., Scott, L.R.: The Mathematical Theory of Finite Element Methods, vol.\u00a015, Springer, (2008)","DOI":"10.1007\/978-0-387-75934-0"},{"issue":"4","key":"3295_CR3","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1007\/s00211-011-0361-8","volume":"117","author":"Y Cao","year":"2011","unstructured":"Cao, Y., Gunzburger, M., He, X., Wang, X.: Robin-Robin domain decomposition methods for the steady-state Stokes-Darcy system with the Beavers-Joseph interface condition. Numer. Math. 117(4), 601\u2013629 (2011)","journal-title":"Numer. Math."},{"issue":"2","key":"3295_CR4","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/PL00005404","volume":"86","author":"A Cohen","year":"2000","unstructured":"Cohen, A., Masson, R.: Wavelet adaptive method for second order elliptic problems: Boundary conditions and domain decomposition. Numer. Math. 86(2), 193\u2013238 (2000)","journal-title":"Numer. Math."},{"key":"3295_CR5","first-page":"350","volume-title":"On the coupling of viscous and inviscid models for incompressible fluid flows via domain decomposition","author":"QV Dinh","year":"1988","unstructured":"Dinh, Q.V., Periaux, J., Terrasson, G., Glowinski, R.: On the coupling of viscous and inviscid models for incompressible fluid flows via domain decomposition, pp. 350\u2013369. International Symposium on Domain Decomposition Methods for Partial Differential Equations, IN (1988)"},{"issue":"3","key":"3295_CR6","doi-asserted-by":"publisher","first-page":"1246","DOI":"10.1137\/06065091X","volume":"45","author":"M Discacciati","year":"2007","unstructured":"Discacciati, M., Quarteroni, A., Valli, A.: Robin-Robin domain decomposition methods for the Stokes-Darcy coupling. SIAM J. Numer. Anal. 45(3), 1246\u20131268 (2007)","journal-title":"SIAM J. Numer. Anal."},{"key":"3295_CR7","doi-asserted-by":"crossref","unstructured":"Dryja, M., Galvis, J., Sarkis, M.: Balancing domain decomposition methods for discontinuous Galerkin discretization, Domain decomposition methods in science and engineering XVII, Springer, pp.\u00a0271\u2013278 (2008)","DOI":"10.1007\/978-3-540-75199-1_31"},{"issue":"3","key":"3295_CR8","first-page":"1001","volume":"28","author":"M Heinkenschloss","year":"2006","unstructured":"Heinkenschloss, M., Nguyen, H.: Neumann-Neumann domain decomposition preconditioners for linear-quadratic elliptic optimal control problems. J. Sci. Comput. 28(3), 1001\u20131028 (2006)","journal-title":"J. Sci. Comput."},{"key":"3295_CR9","doi-asserted-by":"crossref","unstructured":"Kikuchi, N., Oden, J.T.: Contact problems in elasticity: A study of variational inequalities and finite element methods, SIAM, (1988)","DOI":"10.1137\/1.9781611970845"},{"issue":"1","key":"3295_CR10","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1002\/(SICI)1097-0207(19990910)46:1<65::AID-NME663>3.0.CO;2-F","volume":"46","author":"F Kosior","year":"1999","unstructured":"Kosior, F., Guyot, N., Maurice, G.: Analysis of frictional contact problem using boundary element method and domain decomposition method. Int. J. for Numer. Meth. Eng. 46(1), 65\u201382 (1999)","journal-title":"Int. J. for Numer. Meth. Eng."},{"issue":"3","key":"3295_CR11","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1007\/s002110050006","volume":"84","author":"MJ Lai","year":"2000","unstructured":"Lai, M.J., Wenston, P.: On Schwarz\u2019s domain decomposition methods for elliptic boundary value problems. Numer. Math. 84(3), 475\u2013495 (2000)","journal-title":"Numer. Math."},{"key":"3295_CR12","unstructured":"Lions, P.L.: On the Schwarz alternating method. III: a variant for nonoverlapping subdomains, Third international symposium on domain decomposition methods for partial differential equations, vol.\u00a06, SIAM Philadelphia, 202\u2013223 (1990)"},{"issue":"4","key":"3295_CR13","doi-asserted-by":"publisher","first-page":"697","DOI":"10.1007\/s00211-009-0261-3","volume":"114","author":"S Loisel","year":"2010","unstructured":"Loisel, S., Szyld, D.B.: On the geometric convergence of optimized Schwarz methods with applications to elliptic problems. Numer. Math. 114(4), 697\u2013728 (2010)","journal-title":"Numer. Math."},{"issue":"216","key":"3295_CR14","doi-asserted-by":"publisher","first-page":"1387","DOI":"10.1090\/S0025-5718-96-00757-0","volume":"65","author":"J Mandel","year":"1996","unstructured":"Mandel, J., Brezina, M.: Balancing domain decomposition for problems with large jumps in coefficients. Math. Comput. 65(216), 1387\u20131401 (1996)","journal-title":"Math. Comput."},{"key":"3295_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-77209-5","volume-title":"Domain decomposition methods for the numerical solution of partial differential equations","author":"TP Mathew","year":"2008","unstructured":"Mathew, T.P.: Domain decomposition methods for the numerical solution of partial differential equations. Springer, Berlin, Heidelberg (2008)"},{"key":"3295_CR16","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198501787.001.0001","volume-title":"Domain decomposition methods for partial differential equations","author":"A Quarteroni","year":"1999","unstructured":"Quarteroni, A., Valli, A.: Domain decomposition methods for partial differential equations. Oxford University Press, Oxford (1999)"},{"issue":"6","key":"3295_CR17","doi-asserted-by":"publisher","first-page":"1959","DOI":"10.1137\/S1064827500375722","volume":"23","author":"A Quarteroni","year":"2002","unstructured":"Quarteroni, A., Veneziani, A., Zunino, P.: A domain decomposition method for advection-diffusion processes with application to blood solutes. SIAM J. Sci. Comput. 23(6), 1959\u20131980 (2002)","journal-title":"SIAM J. Sci. Comput."},{"issue":"9","key":"3295_CR18","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.70088","volume":"41","author":"O Ruz","year":"2025","unstructured":"Ruz, O., Diaz, J., Vidrascu, M., Moireau, P., Chapelle, D., Fern\u00e1ndez, M.A.: Left heart hemodynamics simulations with fluid-structure interaction and reduced valve modeling. Int. J. Numer. Method Biomed. Eng. 41(9), e70088 (2025)","journal-title":"Int. J. Numer. Method Biomed. Eng."},{"key":"3295_CR19","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1016\/j.apnum.2016.03.002","volume":"105","author":"N Saito","year":"2016","unstructured":"Saito, N., Sugitani, Y., Zhou, G.: Unilateral problem for the Stokes equations: the well-posedness and finite element approximation. Appl. Numer. Math.s 105, 124\u2013147 (2016)","journal-title":"Appl. Numer. Math.s"},{"key":"3295_CR20","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1007\/s002110050292","volume":"77","author":"M Sarkis","year":"1997","unstructured":"Sarkis, M.: Nonstandard coarse spaces and Schwarz methods for elliptic problems with discontinuous coefficients using non-conforming elements. Numer. Math. 77, 383\u2013406 (1997)","journal-title":"Numer. Math."},{"key":"3295_CR21","doi-asserted-by":"crossref","unstructured":"Schenk, K., Hebeker, F.K.: Coupling of two dimensional viscous and inviscid incompressible Stokes equations, Numerical methods for the Navier\u2013Stokes equations: Proceedings of the International Workshop Held at Heidelberg, Springer, 239\u2013248 (1994)","DOI":"10.1007\/978-3-663-14007-8_24"},{"issue":"3","key":"3295_CR22","doi-asserted-by":"publisher","first-page":"1482","DOI":"10.1137\/22M1482846","volume":"61","author":"F Shi","year":"2023","unstructured":"Shi, F., Sun, Y., Zheng, H.: Ensemble domain decomposition algorithm for the fully mixed random Stokes-Darcy model with the Beavers-Joseph interface conditions. SIAM J. Numer. Anal. 61(3), 1482\u20131512 (2023)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"3295_CR23","first-page":"143","volume":"21","author":"A Signorini","year":"1933","unstructured":"Signorini, A.: Sopra alcune questioni di elastostatica. Atti Soc. Ital. Prog. Sci. 21(2), 143\u2013148 (1933)","journal-title":"Atti Soc. Ital. Prog. Sci."},{"issue":"1","key":"3295_CR24","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/BF01385722","volume":"60","author":"BF Smith","year":"1991","unstructured":"Smith, B.F.: A domain decomposition algorithm for elliptic problems in three dimensions. Numer. Math. 60(1), 219\u2013234 (1991)","journal-title":"Numer. Math."},{"key":"3295_CR25","first-page":"225","volume-title":"Domain decomposition methods for partial differential equations","author":"BF Smith","year":"1997","unstructured":"Smith, B.F.: Domain decomposition methods for partial differential equations, pp. 225\u2013243. Springer, Parallel Numerical Algorithms (1997)"},{"key":"3295_CR26","volume-title":"Domain decomposition methods-algorithms and theory","author":"A Toselli","year":"2004","unstructured":"Toselli, A., Widlund, O.: Domain decomposition methods-algorithms and theory. Springer Science & Business Media, Berlin, Heidelberg (2004)"},{"key":"3295_CR27","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1016\/j.cma.2013.09.009","volume":"268","author":"D Vassilev","year":"2014","unstructured":"Vassilev, D., Wang, C., Yotov, I.: Domain decomposition for coupled Stokes and Darcy flows. Comput. Method. Appl. M. 268, 264\u2013283 (2014)","journal-title":"Comput. Method. Appl. M."},{"issue":"4","key":"3295_CR28","doi-asserted-by":"publisher","first-page":"729","DOI":"10.1007\/s00211-023-01348-w","volume":"153","author":"G Zhou","year":"2023","unstructured":"Zhou, G., Jing, F., Kashiwabara, T.: The numerical methods for the coupled fluid flow under the leak interface condition of the friction-type. Numer. Math. 153(4), 729\u2013773 (2023)","journal-title":"Numer. Math."},{"key":"3295_CR29","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1007\/s00021-016-0248-7","volume":"18","author":"G Zhou","year":"2016","unstructured":"Zhou, G., Saito, N.: The Navier-Stokes equations under a unilateral boundary condition of Signorini\u2019s type. J. Math. Fluid Mech. 18, 481\u2013510 (2016)","journal-title":"J. Math. Fluid Mech."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-026-03295-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-026-03295-8","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-026-03295-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T17:43:09Z","timestamp":1777138989000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-026-03295-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,25]]},"references-count":29,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["3295"],"URL":"https:\/\/doi.org\/10.1007\/s10915-026-03295-8","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,25]]},"assertion":[{"value":"15 April 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 January 2026","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 April 2026","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 April 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"76"}}