{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T12:07:44Z","timestamp":1759838864035},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2013,11,26]],"date-time":"2013-11-26T00:00:00Z","timestamp":1385424000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2014,9]]},"DOI":"10.1007\/s10915-013-9806-9","type":"journal-article","created":{"date-parts":[[2013,11,25]],"date-time":"2013-11-25T01:20:58Z","timestamp":1385342458000},"page":"564-583","source":"Crossref","is-referenced-by-count":15,"title":["A Parallel Subgrid Stabilized Finite Element Method Based on Two-Grid Discretization for Simulation of 2D\/3D Steady Incompressible Flows"],"prefix":"10.1007","volume":"60","author":[{"given":"Yueqiang","family":"Shang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shumei","family":"Huang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,11,26]]},"reference":[{"key":"9806_CR1","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/j.parco.2008.11.003","volume":"35","author":"S Behara","year":"2009","unstructured":"Behara, S., Mittal, S.: Parallel finite element computation of incompressible flows. Parallel Comput. 35, 195\u2013212 (2009)","journal-title":"Parallel Comput."},{"key":"9806_CR2","doi-asserted-by":"crossref","first-page":"1790","DOI":"10.1016\/j.jcp.2007.09.026","volume":"227","author":"H Elman","year":"2008","unstructured":"Elman, H., Howle, V.E., Shadid, J., et al.: A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier\u2013Stokes equations. J. Comput. Phys. 227, 1790\u20131808 (2008)","journal-title":"J. Comput. Phys."},{"issue":"7","key":"9806_CR3","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1016\/j.apnum.2010.03.013","volume":"60","author":"YQ Shang","year":"2010","unstructured":"Shang, Y.Q., He, Y.N.: Parallel iterative finite element algorithms based on full domain partition for the stationary Navier\u2013Stokes equations. Appl. Numer. Math. 60(7), 719\u2013737 (2010)","journal-title":"Appl. Numer. Math."},{"key":"9806_CR4","doi-asserted-by":"crossref","first-page":"3543","DOI":"10.1016\/j.jcp.2010.01.015","volume":"229","author":"R Henniger","year":"2010","unstructured":"Henniger, R., Obrist, D., Kleiser, L.: High-order accurate solution of the incompressible Navier\u2013Stokes equations on massively parallel computers. J. Comput. Phys. 229, 3543\u20133572 (2010)","journal-title":"J. Comput. Phys."},{"key":"9806_CR5","first-page":"881","volume":"69","author":"CJ Xu","year":"2000","unstructured":"Xu, C.J., Zhou, A.H.: Local and parallel finite element algorithms based on two-grid discretizations. Math. Comput. 69, 881\u2013909 (2000)","journal-title":"Math. Comput."},{"key":"9806_CR6","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1023\/A:1012284322811","volume":"14","author":"CJ Xu","year":"2001","unstructured":"Xu, C.J., Zhou, A.H.: Local and parallel finite element algorithms based on two-grid discretizations for nonlinear problems. Adv. Comput. Math. 14, 293\u2013327 (2001)","journal-title":"Adv. Comput. Math."},{"issue":"3","key":"9806_CR7","first-page":"227","volume":"24","author":"YN He","year":"2006","unstructured":"He, Y.N., Xu, C.J., Zhou, A.H.: Local and parallel finite element algorithms for the Navier\u2013Stokes problem. J. Comput. Math. 24(3), 227\u2013238 (2006)","journal-title":"J. Comput. Math."},{"issue":"1","key":"9806_CR8","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1007\/s10915-010-9371-4","volume":"44","author":"YN He","year":"2010","unstructured":"He, Y.N., Mei, L.Q., Shang, Y.Q.: Newton iterative parallel finite element algorithm for the steady Navier\u2013Stokes equations. J. Sci. Comput. 44(1), 92\u2013106 (2010)","journal-title":"J. Sci. Comput."},{"key":"9806_CR9","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1016\/j.aml.2010.10.027","volume":"24","author":"YQ Shang","year":"2011","unstructured":"Shang, Y.Q.: A parallel two-level linearization method for incompressible flow problems. Appl. Math. Lett. 24, 364\u2013369 (2011)","journal-title":"Appl. Math. Lett."},{"key":"9806_CR10","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.compfluid.2010.09.009","volume":"40","author":"YQ Shang","year":"2011","unstructured":"Shang, Y.Q., He, Y.N., Luo, Z.D.: A comparison of three kinds of local and parallel finite element algorithms based on two-grid discretizations for the stationary Navier\u2013Stokes equations. Comput. Fluids 40, 249\u2013257 (2011)","journal-title":"Comput. Fluids"},{"key":"9806_CR11","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/j.cma.2011.11.003","volume":"209\u2013212","author":"YQ Shang","year":"2012","unstructured":"Shang, Y.Q., He, Y.N.: A parallel Oseen-linearized algorithm for the stationary Navier\u2013Stokes equations. Comput. Methods Appl. Mech. Eng. 209\u2013212, 172\u2013183 (2012)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9806_CR12","doi-asserted-by":"crossref","first-page":"786","DOI":"10.1016\/j.amc.2005.07.067","volume":"175","author":"YC Ma","year":"2006","unstructured":"Ma, Y.C., Zhang, Z.M., Ren, C.F.: Local and parallel finite element algorithms based on two-grid discretization for the stream function form of Navier\u2013Stokes equations. Appl. Math. Comput. 175, 786\u2013813 (2006)","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"9806_CR13","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s10483-007-0104-x","volume":"28","author":"FY Ma","year":"2007","unstructured":"Ma, F.Y., Ma, C.Y., Wo, W.F.: Local and parallel finite element algorithms based on two-grid discretization for steady Navier\u2013Stokes equations. Appl. Math. Mech. 28(1), 27\u201335 (2007)","journal-title":"Appl. Math. Mech."},{"key":"9806_CR14","doi-asserted-by":"crossref","first-page":"1262","DOI":"10.1016\/j.finel.2011.06.001","volume":"47","author":"YQ Shang","year":"2011","unstructured":"Shang, Y.Q., He, Y.N., Kim, D.W., Zhou, X.J.: A new parallel finite element algorithm for the stationary Navier\u2013Stokes equations. Finite Elem. Anal. Des. 47, 1262\u20131279 (2011)","journal-title":"Finite Elem. Anal. Des."},{"key":"9806_CR15","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1002\/fld.953","volume":"48","author":"E Erturk","year":"2005","unstructured":"Erturk, E., Corke, T., Gokcol, C.: Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers. Int. J. Numer. Methods Fluids 48, 747\u2013774 (2005)","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"9806_CR16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0096-3003(01)00026-1","volume":"129","author":"W Layton","year":"2002","unstructured":"Layton, W., Lee, H., Peterson, J.: A defect-correction method for the incompressible Navier\u2013Stokes equations. Appl. Math. Comput. 129, 1\u201319 (2002)","journal-title":"Appl. Math. Comput."},{"key":"9806_CR17","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1016\/j.cam.2009.12.051","volume":"234","author":"Y Zhang","year":"2010","unstructured":"Zhang, Y., He, Y.N.: Assessment of subgrid-scale models for the incompressible Navier\u2013Stokes equations. J. Comput. Appl. Math. 234, 593\u2013604 (2010)","journal-title":"J. Comput. Appl. Math."},{"key":"9806_CR18","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.jcp.2012.08.024","volume":"233","author":"YQ Shang","year":"2013","unstructured":"Shang, Y.Q.: A two-level subgrid stabilized Oseen iterative method for the steady Navier\u2013Stokes equations. J. Comput. Phys. 233, 210\u2013226 (2013)","journal-title":"J. Comput. Phys."},{"key":"9806_CR19","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1016\/j.jmaa.2013.02.060","volume":"403","author":"YQ Shang","year":"2013","unstructured":"Shang, Y.Q.: A parallel subgrid stabilized finite element method based on fully overlapping domain decomposition for the Navier\u2013Stokes equations. J. Math. Anal. Appl. 403, 667\u2013679 (2013)","journal-title":"J. Math. Anal. Appl."},{"key":"9806_CR20","volume-title":"Sobolev Spaces","author":"R Adams","year":"1975","unstructured":"Adams, R.: Sobolev Spaces. Academic Press, New York (1975)"},{"key":"9806_CR21","doi-asserted-by":"crossref","unstructured":"Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978)","DOI":"10.1115\/1.3424474"},{"key":"9806_CR22","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-61623-5","volume-title":"Finite Element Methods for Navier\u2013Stokes Equations: Theory and Algorithms","author":"V Girault","year":"1986","unstructured":"Girault, V., Raviart, P.A.: Finite Element Methods for Navier\u2013Stokes Equations: Theory and Algorithms. Springer, Berlin (1986)"},{"issue":"2","key":"9806_CR23","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1137\/0719018","volume":"19","author":"JG Heywood","year":"1982","unstructured":"Heywood, J.G., Rannacher, R.: Finite element approximation of the nonstationary Navier\u2013Stokes problem I: regularity of solutions and second-order error estimates for spatial discretization. SIAM J. Numer. Anal. 19(2), 275\u2013311 (1982)","journal-title":"SIAM J. Numer. Anal."},{"key":"9806_CR24","unstructured":"Temam, R.: Navier\u2013Stokes Equations: Theory and Numerical Analysis. North-Holland, Amsterdam (1984)"},{"key":"9806_CR25","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0063447","volume-title":"Finite Element Approximation of the Navier\u2013Stokes Equations","author":"V Girault","year":"1979","unstructured":"Girault, V., Raviart, P.A.: Finite Element Approximation of the Navier\u2013Stokes Equations. Springer, Berlin (1979)"},{"key":"9806_CR26","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1090\/S0025-5718-1974-0373325-9","volume":"28","author":"J Nitsche","year":"1974","unstructured":"Nitsche, J., Schatz, A.H.: Interior estimates for Ritz\u2013Galerkin methods. Math. Comput. 28, 937\u2013955 (1974)","journal-title":"Math. Comput."},{"key":"9806_CR27","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1090\/S0025-5718-1977-0431753-X","volume":"31","author":"AH Schatz","year":"1977","unstructured":"Schatz, A.H., Wahlbin, L.B.: Interior maximum-norm estimates for finite element methods. Math. Comput. 31, 414\u2013442 (1977)","journal-title":"Math. Comput."},{"key":"9806_CR28","first-page":"907","volume":"64","author":"AH Schatz","year":"1995","unstructured":"Schatz, A.H., Wahlbin, L.B.: Interior maximum-norm estimates for finite element methods, part II. Math. Comput. 64, 907\u2013928 (1995)","journal-title":"Math. Comput."},{"key":"9806_CR29","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1051\/m2an\/1995290303671","volume":"29","author":"DN Arnold","year":"1995","unstructured":"Arnold, D.N., Liu, X.: Local error estimates for finite element discretizations of the Stokes equations. RAIRO M2AN 29, 367\u2013389 (1995)","journal-title":"RAIRO M2AN"},{"key":"9806_CR30","unstructured":"Fortin, M.: Calcul num\u00e9rique des ecoulements fluides de Bingham et des fluides Newtoniens incompressible par des m\u00e9thodes d\u2019el\u00e9ments finis. Doctoral thesis, Universit\u00e9 de Paris VI (1972)"},{"key":"9806_CR31","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/0045-7930(73)90027-3","volume":"1","author":"P Hood","year":"1973","unstructured":"Hood, P., Taylor, C.: A numerical solution of the Navier\u2013Stokes equations using the finite element technique. Comput. Fluids 1, 73\u2013100 (1973)","journal-title":"Comput. Fluids"},{"issue":"R\u20133","key":"9806_CR32","first-page":"33","volume":"7","author":"M Crouzeix","year":"1973","unstructured":"Crouzeix, M., Raviart, P.A.: Conforming and nonconforming finite element methods for solving the stationary Stokes equations. RAIRO Anal. Numer. 7(R\u20133), 33\u201376 (1973)","journal-title":"RAIRO Anal. Numer."},{"key":"9806_CR33","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1051\/m2an\/1982160100491","volume":"16","author":"L Mansfield","year":"1982","unstructured":"Mansfield, L.: Finite element subspaces with optimal rates of convergence for stationary Stokes problem. RAIRO Anal. Numer. 16, 49\u201366 (1982)","journal-title":"RAIRO Anal. Numer."},{"issue":"1","key":"9806_CR34","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/S0096-3003(01)00228-4","volume":"133","author":"W Layton","year":"2002","unstructured":"Layton, W.: A connection between subgrid-scale eddy viscosity and mixed methods. Appl. Math. Comput. 133(1), 147\u2013157 (2002)","journal-title":"Appl. Math. Comput."},{"key":"9806_CR35","doi-asserted-by":"crossref","first-page":"1639","DOI":"10.1137\/050623942","volume":"44","author":"S Kaya","year":"2006","unstructured":"Kaya, S., Layton, W., Riviere, B.: Subgrid stabilized defect correction methods for the Navier\u2013Stokes equations. SIAM J. Numer. Anal. 44, 1639\u20131654 (2006)","journal-title":"SIAM J. Numer. Anal."},{"key":"9806_CR36","doi-asserted-by":"crossref","first-page":"5857","DOI":"10.1016\/j.cma.2005.08.016","volume":"195","author":"JL Guermond","year":"2006","unstructured":"Guermond, J.L., Marra, A., Quartapelle, L.: Subgrid stabilized projection method for 2D unsteady flows at high Reynolds numbers. Comput. Methods Appl. Mech. Eng. 195, 5857\u20135876 (2006)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9806_CR37","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/s007910050051","volume":"3","author":"T Hughes","year":"2000","unstructured":"Hughes, T., Mazzei, L., Jansen, K.: Large eddy simulation and the variational multiscale method. Comput. Vis. Sci. 3, 47\u201359 (2000)","journal-title":"Comput. Vis. Sci."},{"key":"9806_CR38","doi-asserted-by":"crossref","first-page":"1485","DOI":"10.1137\/030601533","volume":"26","author":"V John","year":"2005","unstructured":"John, V., Kaya, S.: A finite element variational multiscale method for the Navier\u2013Stokes equations. SIAM J. Sci. Comput. 26, 1485\u20131503 (2005)","journal-title":"SIAM J. Sci. Comput."},{"key":"9806_CR39","doi-asserted-by":"crossref","first-page":"728","DOI":"10.1002\/num.20120","volume":"22","author":"S Kaya","year":"2005","unstructured":"Kaya, S., Rivire, B.: A two-grid stabilization method for solving the steady-state Navier\u2013Stokes equations. Numer. Methods Partial Differ. Equ. 22, 728\u2013743 (2005)","journal-title":"Numer. Methods Partial Differ. Equ."},{"key":"9806_CR40","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.na.2013.02.009","volume":"84","author":"YQ Shang","year":"2013","unstructured":"Shang, Y.Q.: A parallel two-level finite element variational multiscale method for the Navier\u2013Stokes equations. Nonlinear Anal. 84, 103\u2013116 (2013)","journal-title":"Nonlinear Anal."},{"key":"9806_CR41","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1016\/j.cma.2009.01.010","volume":"199","author":"V John","year":"2010","unstructured":"John, V., Kindl, A.: Numerical studies of finite element variational multiscale methods for turbulent flow simulations. Comput. Methods Appl. Mech. Eng. 199, 841\u2013852 (2010)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9806_CR42","unstructured":"Hecht, F., Pironneau, O., Ohtsuka, K.: FreeFem++, Version 3.9-2. http:\/\/www.freefem.org . Accessed 08 Dec 2010"},{"key":"9806_CR43","doi-asserted-by":"crossref","first-page":"1351","DOI":"10.1016\/j.cma.2008.12.001","volume":"198","author":"YN He","year":"2009","unstructured":"He, Y.N., Li, J.: Convergence of three iterative methods based on finite element discretization for the stationary Navier\u2013Stokes equations. Comput. Methods Appl. Mech. Eng. 198, 1351\u20131359 (2009)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"26","key":"9806_CR44","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/0898-1221(93)90318-P","volume":"5","author":"W Layton","year":"1993","unstructured":"Layton, W.: A two level discretization method for the Navier\u2013Stokes equations. Comput. Math. Appl. 5(26), 33\u201338 (1993)","journal-title":"Comput. Math. Appl."},{"key":"9806_CR45","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1016\/0021-9991(82)90058-4","volume":"48","author":"U Ghia","year":"1982","unstructured":"Ghia, U., Ghia, K., Shin, C.: High-Re solutions for incompressible flow using the Navier\u2013Stokes equations and a multigrid method. J. Comput. Phys. 48, 387\u2013411 (1982)","journal-title":"J. Comput. Phys."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-013-9806-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-013-9806-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-013-9806-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,4]],"date-time":"2019-08-04T01:16:00Z","timestamp":1564881360000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-013-9806-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,26]]},"references-count":45,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2014,9]]}},"alternative-id":["9806"],"URL":"https:\/\/doi.org\/10.1007\/s10915-013-9806-9","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,11,26]]}}}