{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:16:27Z","timestamp":1787328987411,"version":"build-2736575974"},"reference-count":83,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11301262"],"award-info":[{"award-number":["11301262"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1418624"],"award-info":[{"award-number":["DMS-1418624"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-FE0009843"],"award-info":[{"award-number":["DE-FE0009843"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>We analyze a parallel, noniterative, multiphysics domain decomposition method for decoupling the Stokes--Darcy model with multistep backward differentiation schemes for the time discretization and finite elements for the spatial discretization. Based on a rigorous analysis of the Ritz projection error shown in this article, we prove almost optimal $L^2$ convergence of the numerical solution. In order to estimate the Ritz projection error on the interface, which plays a key role in the error analysis of the Stokes--Darcy problem, we derive $L^\\infty$ error estimate of the Stokes--Ritz projection under the stress boundary condition for the first time in the literature. The $k$-step backward differentiation schemes, which are important to improve the accuracy in time discretization with unconditional stability, are analyzed in a general framework for any $k\\le 5$. The unconditional stability and high accuracy of these schemes can allow relatively larger time step sizes for given accuracy requirements and hence save a significant amount of computational cost.<\/jats:p>","DOI":"10.1137\/16m1099601","type":"journal-article","created":{"date-parts":[[2018,1,30]],"date-time":"2018-01-30T14:20:39Z","timestamp":1517322039000},"page":"397-427","source":"Crossref","is-referenced-by-count":45,"title":["On Stokes--Ritz Projection and Multistep Backward Differentiation Schemes in Decoupling the Stokes--Darcy Model"],"prefix":"10.1137","volume":"56","author":[{"given":"Max","family":"Gunzburger","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoming","family":"He","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Buyang","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,1,30]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/140962619"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-98-00930-2"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3228"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-015-0702-0"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-011-9427-x"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/s10596-008-9121-y"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/s10596-006-9024-8"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1137\/080727646"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-009-0279-6"},{"key":"atypb10","first-page":"52","volume-title":"Complex Analysis, Joensuu","author":"Bojarski B.","year":"1987"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1137\/110838376"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/080721868"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/136483"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-011-0361-8"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-2014-02779-8"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1137\/080731542"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1515\/JNUM.2008.012"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-009-9274-4"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2014.02.043"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/080740556"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1137\/120897705"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-015-0789-3"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1137\/15M1032156"},{"key":"atypb24","unstructured":"M. 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