{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:21:08Z","timestamp":1787329268363,"version":"build-2736575974"},"reference-count":18,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>In this paper we analyze the family of Yosida algebraic fractional step schemes proposed in [A. Quarteroni, F. Saleri, and A. Veneziani, Comput. Methods Appl. Mech. Engrg., 188 (2000), pp. 505\u2013526], [F. Saleri and A. Veneziani, SIAM J. Numer. Anal., 43 (2005), pp. 174\u2013194], and [P. Gervasio, F. Saleri, and A. Veneziani, J. Comput. Phys., 214 (2006), pp. 347\u2013365] when applied to time-dependent Stokes equations. Under suitable regularity assumptions on the data, splitting error estimates both for velocity and pressure are established. In particular we analyze the first three methods of this family, providing, respectively, convergence (of the fractional step solution towards the numerical solution achieved without any operator splitting) of orders 3\/2, 5\/2, 7\/2 for the velocity and 1, 2, 3 for the pressure. Moreover a general way to set up higher-order schemes is proposed. The present analysis is carried out when spectral element methods are employed for space discretization.<\/jats:p>","DOI":"10.1137\/070682800","type":"journal-article","created":{"date-parts":[[2008,4,11]],"date-time":"2008-04-11T18:08:26Z","timestamp":1207937306000},"page":"1682-1703","source":"Crossref","is-referenced-by-count":9,"title":["Convergence Analysis of High Order Algebraic Fractional Step Schemes for Time-Dependent Stokes Equations"],"prefix":"10.1137","volume":"46","author":[{"given":"Paola","family":"Gervasio","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,4,11]]},"reference":[{"key":"R1","unstructured":"C. Bernardi and Y. Maday,\n                      Approximations Spectrales de Probl\u00e8mes aux Limites Elliptiques\n                      , Springer, Paris, 1992."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(01)00048-4"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang,\n                      Spectral Methods. Fundamentals in Single Domains\n                      , Springer, Heidelberg, 2006.","DOI":"10.1007\/978-3-540-30726-6"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang,\n                      Spectral Methods. Evolution to Complex Geometries and Applications to Fluid Dynamics\n                      , Springer, Heidelberg, 2007.","DOI":"10.1007\/978-3-540-30728-0"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1965.15.1119"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2004037"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-005-9051-y"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2005.09.018"},{"key":"R9","unstructured":"G. Golub and C. V. Loan,\n                      Matrix Computation\n                      , The Johns Hopkins University Press, Baltimore, MD, 1989."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/0719018"},{"key":"R11","unstructured":"Y. Maday and A. Patera,\n                      Spectral element methods for the incompressible Navier-Stokes equations\n                      , in State-of-the-Art Surveys on Computational Mechanics, A. K. Noor and J. T. Oden, ASME, New York, 1989, pp. 71\u2013143."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-7824(99)00027-6"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(99)00192-9"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"A. Quarteroni and A. Valli,\n                      Numerical Approximation of Partial Differential Equations\n                      , Springer, Heidelberg, 1994.","DOI":"10.1007\/978-3-540-85268-1"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142903435429"},{"key":"R16","unstructured":"R. Temam,\n                      Navier\u2013Stokes Equations and Nonlinear Functional Analysis\n                      , CBMS-NSF Regional Conf. Ser. in Appl. Math. 41, SIAM, Philadelphia, PA, 1983."},{"key":"R17","doi-asserted-by":"crossref","unstructured":"F. Zhang,\n                      Matrix Theory\n                      , Springer, New York, 1999.","DOI":"10.1007\/978-1-4757-5797-2"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(00)00032-X"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/070682800","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:13:50Z","timestamp":1787325230000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/070682800"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":18,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/070682800"],"URL":"https:\/\/doi.org\/10.1137\/070682800","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}