{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T11:14:55Z","timestamp":1760267695817,"version":"3.37.3"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"5-6","license":[{"start":{"date-parts":[[2019,11,12]],"date-time":"2019-11-12T00:00:00Z","timestamp":1573516800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,11,12]],"date-time":"2019-11-12T00:00:00Z","timestamp":1573516800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1620262"],"award-info":[{"award-number":["DMS-1620262"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Science Foundation","award":["DMS-1720442"],"award-info":[{"award-number":["DMS-1720442"]}]},{"DOI":"10.13039\/100000181","name":"AFOSR","doi-asserted-by":"crossref","award":["FA9550-16-1-0102"],"award-info":[{"award-number":["FA9550-16-1-0102"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2019,12]]},"DOI":"10.1007\/s10444-019-09729-2","type":"journal-article","created":{"date-parts":[[2019,11,12]],"date-time":"2019-11-12T13:02:57Z","timestamp":1573563777000},"page":"3123-3136","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Stability and convergence analysis of rotational velocity correction methods for the Navier\u2013Stokes equations"],"prefix":"10.1007","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1311-9839","authenticated-orcid":false,"given":"Feng","family":"Chen","sequence":"first","affiliation":[]},{"given":"Jie","family":"Shen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,11,12]]},"reference":[{"issue":"3","key":"9729_CR1","doi-asserted-by":"publisher","first-page":"572","DOI":"10.1016\/j.jcp.2010.10.004","volume":"230","author":"L Botti","year":"2011","unstructured":"Botti, L., Di Pietro, D.A.: A pressure-correction scheme for convection-dominated incompressible flows with discontinuous velocity and continuous pressure. J. Comput. Phys. 230(3), 572\u2013585 (2011)","journal-title":"J. Comput. Phys."},{"key":"9729_CR2","doi-asserted-by":"publisher","first-page":"745","DOI":"10.1090\/S0025-5718-1968-0242392-2","volume":"22","author":"AJ Chorin","year":"1968","unstructured":"Chorin, A.J.: Numerical solution of the Navier-Stokes equations. Math. Comp. 22, 745\u2013762 (1968)","journal-title":"Math. Comp."},{"key":"9729_CR3","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/j.cma.2012.07.023","volume":"247-248","author":"S Dong","year":"2012","unstructured":"Dong, S.: On imposing dynamic contact-angle boundary conditions for wall-bounded liquid-gas flows. Comput. Methods Appl. Mech. Eng. 247-248, 179\u2013200 (2012)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9729_CR4","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1016\/j.jcp.2013.12.042","volume":"261","author":"S Dong","year":"2014","unstructured":"Dong, S., Karniadakis, G.E., Chryssostomidis, C.: A robust and accurate outflow boundary condition for incompressible flow simulations on severely-truncated unbounded domains. J. Comput. Phys. 261, 83\u2013105 (2014)","journal-title":"J. Comput. Phys."},{"issue":"19","key":"9729_CR5","doi-asserted-by":"publisher","first-page":"7013","DOI":"10.1016\/j.jcp.2010.05.037","volume":"229","author":"S Dong","year":"2010","unstructured":"Dong, S., Shen, J.: An unconditionally stable rotational velocity-correction scheme for incompressible flows. J. Comput. Phys. 229(19), 7013\u20137029 (2010)","journal-title":"J. Comput. Phys."},{"issue":"17","key":"9729_CR6","doi-asserted-by":"publisher","first-page":"5788","DOI":"10.1016\/j.jcp.2012.04.041","volume":"231","author":"S Dong","year":"2012","unstructured":"Dong, S., Shen, J.: A time-stepping scheme involving constant coefficient matrices for phase-field simulations of two-phase incompressible flows with large density ratios. J. Comput. Phys. 231(17), 5788\u20135804 (2012)","journal-title":"J. Comput. Phys."},{"issue":"4","key":"9729_CR7","doi-asserted-by":"publisher","first-page":"1017","DOI":"10.1137\/0732047","volume":"32","author":"E Weinan","year":"1995","unstructured":"Weinan, E, Liu, J.-G.: Projection method I: Convergence and numerical boundary layers. SIAM J. Numer. Anal. 32(4), 1017\u20131057 (1995)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"9729_CR8","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1016\/0021-9991(79)90088-3","volume":"30","author":"K Goda","year":"1979","unstructured":"Goda, K.: A multistep technique with implicit difference schemes for calculating two- or three-dimensional cavity flows. J. Comput. Phys. 30(1), 76\u201395 (1979)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"9729_CR9","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1137\/040604418","volume":"43","author":"JL Guermond","year":"2005","unstructured":"Guermond, J.L., Minev, P., Shen, J.: Error analysis of pressure-correction schemes for the time-dependent Stokes equations with open boundary conditions. SIAM J. Numer. Anal. 43(1), 239 (2005)","journal-title":"SIAM J. Numer. Anal."},{"issue":"248","key":"9729_CR10","doi-asserted-by":"publisher","first-page":"1719","DOI":"10.1090\/S0025-5718-03-01621-1","volume":"73","author":"JL Guermond","year":"2003","unstructured":"Guermond, J.L., Shen, J.: On the error estimates for the rotational pressure-correction projection methods. Math. Comput. 73(248), 1719\u20131738 (2003)","journal-title":"Math. Comput."},{"issue":"1","key":"9729_CR11","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1137\/S0036142901395400","volume":"41","author":"JL Guermond","year":"2003","unstructured":"Guermond, J.L., Shen, J.: Velocity-Correction projection methods for incompressible flows. SIAM J. Numer Anal. 41(1), 112\u2013134 (2003)","journal-title":"SIAM J. Numer Anal."},{"issue":"44\u201347","key":"9729_CR12","doi-asserted-by":"publisher","first-page":"6011","DOI":"10.1016\/j.cma.2005.10.010","volume":"195","author":"JL Guermond","year":"2006","unstructured":"Guermond, J.L., Minev, P., Shen, J.: An overview of projection methods for incompressible flows. Comput. Methods Appl. Mech. Eng. 195(44\u201347), 6011\u20136045 (2006)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"2","key":"9729_CR13","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1137\/0727022","volume":"27","author":"JG Heywood","year":"1990","unstructured":"Heywood, J.G., Rannacher, R.: Finite-element approximation of the nonstationary Navier-Stokes problem part IV: Error analysis for second-order time discretization. SIAM J. Numer. Anal. 27(2), 353\u2013384 (1990)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"9729_CR14","doi-asserted-by":"publisher","first-page":"414","DOI":"10.1016\/0021-9991(91)90007-8","volume":"97","author":"GE Karniadakis","year":"1991","unstructured":"Karniadakis, G.E., Israeli, M., Orszag, S.A.: High-order splitting methods for the incompressible Navier-Stokes equations. J. Comput. Phys. 97(2), 414\u2013443 (1991)","journal-title":"J. Comput. Phys."},{"key":"9729_CR15","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1016\/j.cma.2016.05.043","volume":"309","author":"S Lee","year":"2016","unstructured":"Lee, S., Salgado, A.J.: Stability analysis of pressure correction schemes for the Navier-Stokes equations with traction boundary conditions. Comput. Methods Appl. Mech. Eng. 309, 307\u2013324 (2016)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"250","key":"9729_CR16","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1090\/S0025-5718-04-01687-4","volume":"74","author":"H Ricardo Nochetto","year":"2005","unstructured":"Ricardo Nochetto, H., Pyo, J.-H.: Error estimates for semi-discrete Gauge methods for the Navier-Stokes equations. Math. Comput. 74(250), 521\u2013542 (2005)","journal-title":"Math. Comput."},{"issue":"1","key":"9729_CR17","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/BF01061454","volume":"1","author":"SA Orszag","year":"1986","unstructured":"Orszag, S.A., Israeli, M., Deville, M.O.: Boundary conditions for incompressible flows. J. Sci. Comput. 1(1), 75\u2013111 (1986)","journal-title":"J. Sci. Comput."},{"issue":"1","key":"9729_CR18","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1016\/j.jcp.2006.06.013","volume":"221","author":"J-H Pyo","year":"2007","unstructured":"Pyo, J.-H., Shen, J.: Gauge-Uzawa methods for incompressible flows with variable density. J. Comput. Phys. 221(1), 181\u2013197 (2007)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"9729_CR19","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1137\/0729004","volume":"29","author":"Jie Shen","year":"1992","unstructured":"Shen, J.: On error estimates of projection methods for Navier-Stokes equations: First-order schemes. SIAM J. Numer. Anal., 57\u201377 (1992)","journal-title":"SIAM Journal on Numerical Analysis"},{"issue":"215","key":"9729_CR20","doi-asserted-by":"publisher","first-page":"1039","DOI":"10.1090\/S0025-5718-96-00750-8","volume":"65","author":"J Shen","year":"1996","unstructured":"Shen, J.: On error estimates of the projection methods for the Navier-Stokes equations: Second-order schemes. Math. Comput. 65(215), 1039\u20131066 (1996)","journal-title":"Math. Comput."},{"key":"9729_CR21","doi-asserted-by":"publisher","first-page":"1489","DOI":"10.1137\/0915089","volume":"15","author":"JS Efficient","year":"1994","unstructured":"Efficient, J.S.: spectral-Galerkin method I. Direct solvers for second- and fourth-order equations by using Legendre polynomials. SIAM J. Sci. Comput. 15, 1489\u20131505 (1994)","journal-title":"SIAM J. Sci. Comput."},{"key":"9729_CR22","doi-asserted-by":"crossref","unstructured":"Dinesh, A., Shetty, J.S., Chandy, A.J., Frankel, S.H.: A pressure-correction scheme for rotational Navier-Stokes equations and its application to rotating turbulent flows. Communications in Computational Physics (2010)","DOI":"10.4208\/cicp.301109.040310s"},{"issue":"1","key":"9729_CR23","first-page":"70","volume":"8","author":"H Sun","year":"2011","unstructured":"Sun, H., He, Y., Feng, X.: On error estimates of the pressure-correction projection methods for the time-dependent Navier-Stokes equations. Int. J. Numer. Anal. Model 8(1), 70\u201385 (2011)","journal-title":"Int. J. Numer. Anal. Model"},{"key":"9729_CR24","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1007\/BF00247696","volume":"33","author":"R Temam","year":"1969","unstructured":"Temam, R.: Sur l\u2019approximation de la solution des \u00e9quations de Navier-Stokes par la m\u00e9thode des pas fractionnaires (ii). Arch. Rational Mech. Anal. 33, 377\u2013385 (1969)","journal-title":"Arch. Rational Mech. Anal."},{"issue":"7","key":"9729_CR25","doi-asserted-by":"publisher","first-page":"673","DOI":"10.1002\/(SICI)1097-0363(19960415)22:7<673::AID-FLD373>3.0.CO;2-O","volume":"22","author":"L. J. P. TIMMERMANS","year":"1996","unstructured":"Timmermans, L.J.P., Minev, P.D., Van De Vosse, F.N.: An approximate projection scheme for incompressible flow using spectral elements. Int. J. Numer. Methods fluids 22(7), 673\u2013688 (1996)","journal-title":"International Journal for Numerical Methods in Fluids"},{"issue":"3","key":"9729_CR26","doi-asserted-by":"publisher","first-page":"870","DOI":"10.1137\/0907059","volume":"7","author":"J van Kan","year":"1986","unstructured":"van Kan, J.: A second-order accurate pressure-correction scheme for viscous incompressible flow. SIAM J. Sci. Stat. Comput. 7(3), 870\u2013891 (1986)","journal-title":"SIAM J. Sci. Stat. Comput."},{"issue":"23","key":"9729_CR27","doi-asserted-by":"publisher","first-page":"8573","DOI":"10.1016\/j.jcp.2011.08.009","volume":"230","author":"X Zheng","year":"2011","unstructured":"Zheng, X., Dong, S.: An eigen-based high-order expansion basis for structured spectral elements. J. Comput. Phys. 230(23), 8573\u20138602 (2011)","journal-title":"J. Comput. Phys."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-019-09729-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-019-09729-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-019-09729-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,11]],"date-time":"2020-11-11T00:54:57Z","timestamp":1605056097000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-019-09729-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,12]]},"references-count":27,"journal-issue":{"issue":"5-6","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["9729"],"URL":"https:\/\/doi.org\/10.1007\/s10444-019-09729-2","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"type":"print","value":"1019-7168"},{"type":"electronic","value":"1572-9044"}],"subject":[],"published":{"date-parts":[[2019,11,12]]},"assertion":[{"value":"5 September 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 September 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 November 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}