{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,5,8]],"date-time":"2023-05-08T05:40:58Z","timestamp":1683524458495},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2022,11,15]],"date-time":"2022-11-15T00:00:00Z","timestamp":1668470400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,11,15]],"date-time":"2022-11-15T00:00:00Z","timestamp":1668470400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12172202"],"award-info":[{"award-number":["12172202"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11701343"],"award-info":[{"award-number":["11701343"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12101494"],"award-info":[{"award-number":["12101494"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2021MA063"],"award-info":[{"award-number":["ZR2021MA063"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007128","name":"Natural Science Foundation of Shaanxi Province","doi-asserted-by":"publisher","award":["2021JQ-426"],"award-info":[{"award-number":["2021JQ-426"]}],"id":[{"id":"10.13039\/501100007128","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Scientific Research Program of Shaanxi Provincial Education Department","award":["21JK0935"],"award-info":[{"award-number":["21JK0935"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2023,6]]},"DOI":"10.1007\/s11075-022-01442-4","type":"journal-article","created":{"date-parts":[[2022,11,15]],"date-time":"2022-11-15T09:02:41Z","timestamp":1668502961000},"page":"815-831","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A modified local and parallel finite element method for the coupled Stokes-Darcy model with the Beavers-Joseph interface condition"],"prefix":"10.1007","volume":"93","author":[{"given":"Xinhui","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guangzhi","family":"Du","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,11,15]]},"reference":[{"issue":"4","key":"1442_CR1","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":"288","key":"1442_CR2","doi-asserted-by":"publisher","first-page":"1617","DOI":"10.1090\/S0025-5718-2014-02779-8","volume":"83","author":"Y Cao","year":"2014","unstructured":"Cao, Y., Gunzburger, M., He, X., Wang, X.: Parallel, non-iterative, multi-physics domain decomposition methods for time-dependent Stokes-Darcy systems. Math. Comput. 83(288), 1617\u20131644 (2014)","journal-title":"Math. Comput."},{"issue":"1","key":"1442_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.4310\/CMS.2010.v8.n1.a2","volume":"8","author":"Y Cao","year":"2010","unstructured":"Cao, Y., Gunzburger, M., Hua, F., Wang, X.: Coupled Stokes-Darcy model with Beavers-Joseph interface boundary condition. Commun. Math. Sci. 8(1), 1\u201325 (2010)","journal-title":"Commun. Math. Sci."},{"issue":"3","key":"1442_CR4","doi-asserted-by":"publisher","first-page":"1064","DOI":"10.1137\/080740556","volume":"49","author":"W Chen","year":"2011","unstructured":"Chen, W., Gunzburger, M., Hua, F., Wang, X.: A parallel Robin-Robin domain decomposition method for the Stokes-Darcy system. SIAM J. Numer. Anal. 49(3), 1064\u20131084 (2011)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"1442_CR5","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."},{"issue":"1","key":"1442_CR6","first-page":"39","volume":"29","author":"G Du","year":"2021","unstructured":"Du, G., Zuo, L.: A two-grid method with backtracking for the mixed Stokes\/Darcy model. J. Numer. Math. 29(1), 39\u201346 (2021)","journal-title":"J. Numer. Math."},{"issue":"6","key":"1442_CR7","doi-asserted-by":"publisher","first-page":"1601","DOI":"10.1002\/num.22493","volume":"36","author":"G Du","year":"2020","unstructured":"Du, G., Li, Q., Zhang, Y.: A two-grid method with backtracking for the mixed Navier-Stokes\/Darcy model. Numer. Methods Partial Diff. Equa. 36(6), 1601\u20131610 (2020)","journal-title":"Numer. Methods Partial Diff. Equa."},{"issue":"3","key":"1442_CR8","doi-asserted-by":"publisher","first-page":"1445","DOI":"10.1007\/s10915-017-0593-6","volume":"75","author":"G Du","year":"2018","unstructured":"Du, G., Zuo, L.: A parallel partition of unity scheme based on two-grid discretizations for the Navier-Stokes problem. J. Sci. Comput. 75(3), 1445\u20131462 (2018)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"1442_CR9","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1007\/s10915-020-01348-0","volume":"85","author":"G Du","year":"2020","unstructured":"Du, G., Zuo, L.: A parallel iterative finite element method for the linear elliptic equations. J. Sci. Comput. 85(2), 35 (2020)","journal-title":"J. Sci. Comput."},{"issue":"1","key":"1442_CR10","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1007\/s10915-021-01723-5","volume":"90","author":"G Du","year":"2022","unstructured":"Du, G., Zuo, L., Zhang, Y.: A new local and parallel finite element method for the coupled Stokes-Darcy model. J. Sci. Comput. 90(1), 43 (2022)","journal-title":"J. Sci. Comput."},{"issue":"5","key":"1442_CR11","doi-asserted-by":"publisher","first-page":"1331","DOI":"10.1016\/S0252-9602(17)30076-0","volume":"37","author":"G Du","year":"2017","unstructured":"Du, G., Zuo, L.: Local and parallel finite element method for the mixed Navier-Stokes\/Darcy model with Beavers-Joseph interface conditions. Acta Math. Sci. 37(5), 1331\u20131347 (2017)","journal-title":"Acta Math. Sci."},{"key":"1442_CR12","doi-asserted-by":"crossref","unstructured":"Du, G., Zuo, L.: Local and parallel finite element methods for the coupled Stokes\/Darcy model. Numer. Algor., 1593-1611 (2021)","DOI":"10.1007\/s11075-020-01021-5"},{"issue":"2","key":"1442_CR13","doi-asserted-by":"publisher","first-page":"572","DOI":"10.1007\/s10473-020-0218-2","volume":"40B","author":"G Du","year":"2020","unstructured":"Du, G.: Expandable parallel finite element methods for linear elliptic problems. Acta Math. Sci. 40B(2), 572\u2013588 (2020)","journal-title":"Acta Math. Sci."},{"key":"1442_CR14","doi-asserted-by":"crossref","unstructured":"Du, G., Zuo, L.: Local and parallel finite element post-processing scheme for the Stokes problem. Comput. Math. Applic., 129\u2013140 (2017)","DOI":"10.1016\/j.camwa.2016.11.002"},{"key":"1442_CR15","unstructured":"He, Y., Xu, J., Zhou, A.: Local and parallel finite element algorithms for the Navier-Stokes problem. J. Comput. Math., 227\u2013238 (2006)"},{"issue":"3","key":"1442_CR16","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1007\/s00211-008-0141-2","volume":"109","author":"Y He","year":"2008","unstructured":"He, Y., Xu, J., Zhou, A., Li, J.: Local and parallel finite element algorithms for the Stokes problem. Numer. Math. 109(3), 415\u2013434 (2008)","journal-title":"Numer. Math."},{"key":"1442_CR17","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1016\/j.aml.2016.01.007","volume":"57","author":"Y Hou","year":"2016","unstructured":"Hou, Y.: Optimal error estimates of a decoupled scheme based on two-grid finite element for mixed Stokes-Darcy model. Appl. Math. Lett. 57, 90\u201396 (2016)","journal-title":"Appl. Math. Lett."},{"issue":"9-12","key":"1442_CR18","doi-asserted-by":"publisher","first-page":"947","DOI":"10.1016\/j.cma.2008.11.001","volume":"198","author":"B Jiang","year":"2009","unstructured":"Jiang, B.: A parallel domain decomposition method for coupling of surface and groundwater flows. Comput. Methods Appl. Mech. Eng. 198(9-12), 947\u2013957 (2009)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"4","key":"1442_CR19","doi-asserted-by":"publisher","first-page":"1915","DOI":"10.1007\/s11075-021-01100-1","volume":"88","author":"Q Li","year":"2021","unstructured":"Li, Q., Du, G.: Local and parallel finite element methods based on two-grid discretizations for the nonstationary Navier-Stokes equations. Numer. Algor. 88(4), 1915\u20131936 (2021)","journal-title":"Numer. Algor."},{"issue":"6","key":"1442_CR20","doi-asserted-by":"publisher","first-page":"3023","DOI":"10.1002\/num.22813","volume":"37","author":"Q Li","year":"2021","unstructured":"Li, Q., Du, G.: Local and parallel finite element methods based on two-grid discretizations for unsteady convection-diffusion problem. Numer. Methods Partial Diff. Equa. 37(6), 3023\u20133041 (2021)","journal-title":"Numer. Methods Partial Diff. Equa."},{"key":"1442_CR21","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1016\/j.cam.2017.11.011","volume":"334","author":"R Li","year":"2018","unstructured":"Li, R., Gao, Y., Li, J., Chen, Z.: A weak galerkin finite element method for a coupled Stokes-Darcy problem on general meshes. J. Comput. Appl. Math. 334, 111\u2013127 (2018)","journal-title":"J. Comput. Appl. Math."},{"key":"1442_CR22","doi-asserted-by":"publisher","first-page":"112923","DOI":"10.1016\/j.cma.2020.112923","volume":"364","author":"Y Li","year":"2020","unstructured":"Li, Y., Hou, Y., Layton, W., Zhao, H.: Adaptive partitioned method for the time-accurate approximation of the evolutionary Stokes-Darcy system. Comput. Methods Appl. Mech. Eng. 364, 112923 (2020)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"5","key":"1442_CR23","doi-asserted-by":"publisher","first-page":"1801","DOI":"10.1137\/050637820","volume":"45","author":"M Mu","year":"2007","unstructured":"Mu, M., Xu, J.: A two-grid method of a mixed Stokes-Darcy model for coupling fluid flow with porous media flow. SIAM J. Numer. Anal. 45 (5), 1801\u20131813 (2007)","journal-title":"SIAM J. Numer. Anal."},{"issue":"9","key":"1442_CR24","doi-asserted-by":"publisher","first-page":"817","DOI":"10.1016\/j.camwa.2019.07.032","volume":"73","author":"Y Qin","year":"2020","unstructured":"Qin, Y., Hou, Y., Huang, P., Wang, Y.: Numerical analysis of two grad-div stabilization methods for the time-dependent Stokes\/Darcy model. Comput. Math. Applic. 73(9), 817\u2013832 (2020)","journal-title":"Comput. Math. Applic."},{"issue":"2","key":"1442_CR25","doi-asserted-by":"publisher","first-page":"813","DOI":"10.1137\/110828095","volume":"51","author":"L Shan","year":"2013","unstructured":"Shan, L., Zheng, H.: Partitioned time stepping method for fully evolutionary Stokes-Darcy flow with Beavers-Joseph interface conditions. SIAM J. Numer. Anal. 51(2), 813\u2013839 (2013)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"1442_CR26","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1007\/s11075-009-9330-z","volume":"54","author":"Y Shang","year":"2010","unstructured":"Shang, Y., Wang, K.: Local and parallel finite element algorithms based on two-grid discretizations for the transient Stokes equations. Numer. Algor. 54(2), 195\u2013218 (2010)","journal-title":"Numer. Algor."},{"issue":"7","key":"1442_CR27","doi-asserted-by":"publisher","first-page":"719","DOI":"10.1016\/j.apnum.2010.03.013","volume":"60","author":"Y Shang","year":"2010","unstructured":"Shang, Y., He, Y.: Parallel iterative finite element algorithms based on full domain partition for the stationary Navier-Stokes equations. Appl. Numer. Math. 60(7), 719\u2013737 (2010)","journal-title":"Appl. Numer. Math."},{"issue":"11","key":"1442_CR28","doi-asserted-by":"publisher","first-page":"1262","DOI":"10.1016\/j.finel.2011.06.001","volume":"47","author":"Y Shang","year":"2011","unstructured":"Shang, Y., He, Y., Kim, D., Zhou, X.: A new parallel finite element algorithm for the stationary Navier-Stokes equations. Finite Elem. Anal. Des. 47(11), 1262\u20131279 (2011)","journal-title":"Finite Elem. Anal. Des."},{"issue":"6","key":"1442_CR29","doi-asserted-by":"publisher","first-page":"1726","DOI":"10.1016\/j.camwa.2020.08.004","volume":"80","author":"L Song","year":"2020","unstructured":"Song, L., Li, P., Gu, Y., Fan, C.: Generalized finite difference method for solving stationary 2D and 3D stokes equations with a mixed boundary condition. Comput. Math. Applic. 80(6), 1726\u20131743 (2020)","journal-title":"Comput. Math. Applic."},{"key":"1442_CR30","doi-asserted-by":"publisher","first-page":"113578","DOI":"10.1016\/j.cma.2020.113578","volume":"374","author":"Y Sun","year":"2021","unstructured":"Sun, Y., Sun, W., Zheng, H.: Domain decomposition method for the fully-mixed Stokes-Darcy coupled problem. Comput. Methods Appl. Mech. Eng. 374, 113578 (2021)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"1442_CR31","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. Methods Appl. Mech. Eng. 268, 264\u2013283 (2014)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"15","key":"1442_CR32","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1016\/j.camwa.2021.03.019","volume":"90","author":"X Wang","year":"2021","unstructured":"Wang, X., Du, G., Zuo, L.: A novel local and parallel finite element method for the mixed Navier-Stokes-Darcy problem. Comput. Math. Applic. 90 (15), 73\u201379 (2021)","journal-title":"Comput. Math. Applic."},{"issue":"231","key":"1442_CR33","doi-asserted-by":"publisher","first-page":"881","DOI":"10.1090\/S0025-5718-99-01149-7","volume":"69","author":"J Xu","year":"2000","unstructured":"Xu, J., Zhou, A.: Local and parallel finite element algorithms based on two-grid discretizations. Math. Comput. 69(231), 881\u2013909 (2000)","journal-title":"Math. Comput."},{"issue":"5","key":"1442_CR34","doi-asserted-by":"publisher","first-page":"C547","DOI":"10.1137\/130925748","volume":"36","author":"J Yu","year":"2014","unstructured":"Yu, J., Shi, F., Zheng, H.: Local and parallel finite element algorithms based on the partition of unity for the Stokes problem. SIAM J. Sci. Comput. 36(5), C547\u2013C567 (2014)","journal-title":"SIAM J. Sci. Comput."},{"key":"1442_CR35","doi-asserted-by":"publisher","first-page":"106588","DOI":"10.1016\/j.aml.2020.106588","volume":"110","author":"J Yu","year":"2020","unstructured":"Yu, J., Sun, Y., Shi, F., Zheng, H.: Nitsches type stabilized finite element method for the fully mixed Stokes-Darcy problem with Beavers-Joseph conditions. Appl. Math. Lett. 110, 106588 (2020)","journal-title":"Appl. Math. Lett."},{"issue":"2","key":"1442_CR36","doi-asserted-by":"publisher","first-page":"512","DOI":"10.1007\/s10915-014-9979-x","volume":"65","author":"H Zheng","year":"2015","unstructured":"Zheng, H., Yu, J., Shi, F.: Local and parallel finite element method based on the partition of unity for incompressible flow. J. Sci. Comput. 65(2), 512\u2013532 (2015)","journal-title":"J. Sci. Comput."},{"issue":"4","key":"1442_CR37","doi-asserted-by":"publisher","first-page":"937","DOI":"10.1007\/s10444-014-9392-x","volume":"41","author":"H Zheng","year":"2015","unstructured":"Zheng, H., Song, L., Hou, Y., Zhang, Y.: The partition of unity parallel finite element algorithm. Adv. Comput. Math. 41(4), 937\u2013951 (2015)","journal-title":"Adv. Comput. Math."},{"issue":"1","key":"1442_CR38","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1007\/s11075-017-0308-y","volume":"77","author":"L Zuo","year":"2018","unstructured":"Zuo, L., Du, G.: A parallel two-grid linearized method for the coupled Navier-Stokes-Darcy problem. Numer. Algor. 77(1), 151\u2013165 (2018)","journal-title":"Numer. Algor."},{"issue":"11","key":"1442_CR39","doi-asserted-by":"publisher","first-page":"4012","DOI":"10.1016\/j.camwa.2018.03.010","volume":"75","author":"L Zuo","year":"2018","unstructured":"Zuo, L., Du, G.: A multi-grid technique for coupling fluid flow with porous media flow. Comput. Math. Applic. 75(11), 4012\u20134021 (2018)","journal-title":"Comput. Math. Applic."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-022-01442-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-022-01442-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-022-01442-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,8]],"date-time":"2023-05-08T05:11:16Z","timestamp":1683522676000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-022-01442-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,15]]},"references-count":39,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["1442"],"URL":"https:\/\/doi.org\/10.1007\/s11075-022-01442-4","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,15]]},"assertion":[{"value":"15 February 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 October 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 November 2022","order":3,"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 no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"<!--Emphasis Type='Bold' removed-->Conflict of interest"}}]}}