{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T11:07:12Z","timestamp":1760267232836},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2013,5,17]],"date-time":"2013-05-17T00:00:00Z","timestamp":1368748800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2014,1]]},"DOI":"10.1007\/s00211-013-0556-2","type":"journal-article","created":{"date-parts":[[2013,5,16]],"date-time":"2013-05-16T08:23:01Z","timestamp":1368692581000},"page":"75-101","source":"Crossref","is-referenced-by-count":23,"title":["Optimal $$L^2, H^1$$ L 2 , H 1 and $$L^\\infty $$ L \u221e analysis of finite volume methods for the stationary Navier\u2013Stokes equations with large data"],"prefix":"10.1007","volume":"126","author":[{"given":"Jian","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhangxin","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,5,17]]},"reference":[{"key":"556_CR1","volume-title":"Sobolev spaces","author":"RA Adams","year":"1975","unstructured":"Adams, R.A.: Sobolev spaces. Academic Press, New York (1975)"},{"key":"556_CR2","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1137\/0724050","volume":"24","author":"RE Bank","year":"1987","unstructured":"Bank, R.E., Rose, D.J.: Some error estimates for the box method. SIAM J. Numer. Anal. 24, 777\u2013787 (1987)","journal-title":"SIAM J. Numer. Anal."},{"key":"556_CR3","volume-title":"The mathematical theory of finite elements","author":"S Brenner","year":"1991","unstructured":"Brenner, S., Scott, L.R.: The mathematical theory of finite elements. Springer, New York (1991)"},{"key":"556_CR4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01395985","volume":"36","author":"F Brezzi","year":"1980","unstructured":"Brezzi, F., Rappaz, J., Raviart, P.-A.: Finite element approximation of nonlinear problems. Part I: Branch of nonsingular solutions. Numer. Math. 36, 1\u201325 (1980)","journal-title":"Numer. Math."},{"key":"556_CR5","volume-title":"Finite element methods and their applications","author":"Z Chen","year":"2005","unstructured":"Chen, Z.: Finite element methods and their applications. Spring, Heidelberg (2005)"},{"key":"556_CR6","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1023\/A:1014577215948","volume":"16","author":"Z Chen","year":"2002","unstructured":"Chen, Z., Li, R., Zhou, A.: A note on the optimal $$L^2$$ L 2 -estimate of finite volume element method. Adv Comput Math 16, 291\u2013303 (2002)","journal-title":"Adv Comput Math"},{"key":"556_CR7","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1002\/(SICI)1098-2426(199703)13:2<147::AID-NUM2>3.0.CO;2-P","volume":"13","author":"SH Chou","year":"1997","unstructured":"Chou, S.H., Kwak, D.Y.: Analysis and convergence of a MAC scheme for the generalized Stokes problem. Numer. Meth. Partial Diff. Equ. 13, 147\u2013162 (1997)","journal-title":"Numer. Meth. Partial Diff. Equ."},{"key":"556_CR8","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1137\/S0036142996299964","volume":"35","author":"SH Chou","year":"1998","unstructured":"Chou, S.H., Kwak, D.Y.: A covolume method based on rotated bilinears for the generalized Stokes problem. SIAM J. Numer. Anal. 35, 494\u2013507 (1998)","journal-title":"SIAM J. Numer. Anal."},{"key":"556_CR9","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1090\/S0025-5718-99-01192-8","volume":"69","author":"SH Chou","year":"2000","unstructured":"Chou, S.H., Li, Q.: Error estimates in $$L^2, H^1$$ L 2 , H 1 and $$L^{\\infty }$$ L \u221e in co-volume methods for elliptic and parabolic problems: a unified approach. Math. Comp. 69, 103\u2013120 (2000)","journal-title":"Math. Comp."},{"key":"556_CR10","volume-title":"The finite element method for elliptic problems","author":"PG Ciarlet","year":"1978","unstructured":"Ciarlet, P.G.: The finite element method for elliptic problems. North-Holland, Amsterdam (1978)"},{"key":"556_CR11","doi-asserted-by":"crossref","first-page":"491","DOI":"10.2307\/2008760","volume":"15","author":"R Duran","year":"1988","unstructured":"Duran, R., Nochetto, R., Wang, J.: Sharp maximum norm error estimates for finite element approximations of the Stokes problem in 2-D. Math. Comp. 15, 491\u2013506 (1988)","journal-title":"Math. Comp."},{"key":"556_CR12","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1002\/(SICI)1098-2426(200005)16:3<285::AID-NUM2>3.0.CO;2-3","volume":"16","author":"RE Ewing","year":"2000","unstructured":"Ewing, R.E., Lazarov, R.D., Lin, Y.: Finite volume element approximations of nonlocal reactive flows in porous media. Numer. Methods Partial Differ. Equ. 16, 285\u2013311 (2000)","journal-title":"Numer. Methods Partial Differ. Equ."},{"key":"556_CR13","doi-asserted-by":"crossref","first-page":"1865","DOI":"10.1137\/S0036142900368873","volume":"39","author":"RE Ewing","year":"2002","unstructured":"Ewing, R.E., Lin, T., Lin, Y.: On the accuracy of the finite volume element method based on piecewise linear polynomials. SIAM J. Numer. Anal. 39, 1865\u20131888 (2002)","journal-title":"SIAM J. Numer. Anal."},{"key":"556_CR14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/040613081","volume":"45","author":"R Eymard","year":"2007","unstructured":"Eymard, R., Herbin, R., Latch\u00e9, J.C.: Convergence analysis of a colocated finite volume scheme for the incompressible Navier\u2013Stokes equations on general 2D or 3D meshes. SIAM J. Numer. Anal. 45, 1\u201336 (2007)","journal-title":"SIAM J. Numer. Anal."},{"key":"556_CR15","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1002\/(SICI)1098-2426(200005)16:3<285::AID-NUM2>3.0.CO;2-3","volume":"16","author":"J Frehse","year":"2000","unstructured":"Frehse, J., Rannacher, R.: Finite volume element approximations of nonlocal reactive flows in porous media. Numer. Methods Partial Differ. Equ. 16, 285\u2013311 (2000)","journal-title":"Numer. Methods Partial Differ. Equ."},{"key":"556_CR16","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/j.matpur.2004.09.017","volume":"84","author":"V Girault","year":"2005","unstructured":"Girault, V., Nochetto, R.H., Scott, R.: Maximum-norm stability of the finite element Stokes projection. J. Math. Pures Appl. 84, 279\u2013330 (2005)","journal-title":"J. Math. Pures Appl."},{"key":"556_CR17","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)"},{"key":"556_CR18","doi-asserted-by":"crossref","first-page":"1503","DOI":"10.1016\/j.apnum.2007.08.005","volume":"58","author":"Y He","year":"2008","unstructured":"He, Y., Li, J.: A stabilized finite element method based on local polynomial pressure projection for the stationary Navier\u2013Stokes equation. Appl. Numer. Math. 58, 1503\u20131514 (2008)","journal-title":"Appl. Numer. Math."},{"key":"556_CR19","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, 275\u2013311 (1982)","journal-title":"SIAM J. Numer. Anal."},{"key":"556_CR20","doi-asserted-by":"crossref","first-page":"1762","DOI":"10.1137\/S0036142994264699","volume":"35","author":"J Huang","year":"1998","unstructured":"Huang, J., Xi, S.: On the finite volume element method for general self-adjoint elliptic problems. SIAM J. Numer. Anal. 35, 1762\u20131774 (1998)","journal-title":"SIAM J. Numer. Anal."},{"key":"556_CR21","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/s10444-007-9060-5","volume":"30","author":"J Li","year":"2009","unstructured":"Li, J., Chen, Z.: A new stabilized finite volume method for the stationary Stokes equations. Adv. Comp. Math. 30, 141\u2013152 (2009)","journal-title":"Adv. Comp. Math."},{"key":"556_CR22","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/s00211-012-0462-z","volume":"122","author":"J Li","year":"2012","unstructured":"Li, J., Chen, Z., He, Y.: A stabilized multi-level method for non-singular finite volume solutions of the stationary 3D Navier\u2013Stokes equations. Numer. Math. 122, 279\u2013304 (2012)","journal-title":"Numer. Math."},{"key":"556_CR23","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1007\/s10543-010-0277-1","volume":"50","author":"J Li","year":"2010","unstructured":"Li, J., Shen, L., Chen, Z.: Convergence and stability of a stabilized finite volume method for the stationary Navier\u2013Stokes equations. BIT Numer. Math. 50, 823\u2013842 (2010)","journal-title":"BIT Numer. Math."},{"key":"556_CR24","unstructured":"Li, J., Zhao, X., Wu, J.: Study of stabilization of the lower order finite volume methods for the incompressible flows. Acta Math. Sinica 56 (2013) (in Chinese)"},{"key":"556_CR25","first-page":"140","volume":"2","author":"R Li","year":"1982","unstructured":"Li, R., Zhu, P.: Generalized difference methods for second order elliptic partial differential equations (I)-triangle grids. Numer. Math. J. Chinese Univ. 2, 140\u2013152 (1982)","journal-title":"Numer. Math. J. Chinese Univ."},{"key":"556_CR26","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1137\/0724007","volume":"24","author":"R Li","year":"1987","unstructured":"Li, R.: Generalized difference methods for a nonlinear Dirichlet problem. SIAM J. Numer. Anal. 24, 77\u201388 (1987)","journal-title":"SIAM J. Numer. Anal."},{"key":"556_CR27","unstructured":"Silvester, D.J.: Stabilised mixed finite element methods. Numerical Analysis, Report No. 262 (1995)"},{"key":"556_CR28","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1090\/S0025-5718-1982-0645661-4","volume":"38","author":"R Rannacher","year":"1982","unstructured":"Rannacher, R., Scott, R.: Some optimal error estimates for piecewise linear finite element approximations. Math. Comp. 38, 437\u2013445 (1982)","journal-title":"Math. Comp."},{"key":"556_CR29","first-page":"9","volume":"42","author":"R Stenberg","year":"1984","unstructured":"Stenberg, R.: Analysis of mixed finite element methods for the Stokes problem: a unified approach. Math. Comp. 42, 9\u201323 (1984)","journal-title":"Math. Comp."},{"key":"556_CR30","volume-title":"Navier\u2013Stokes equations","author":"R Temam","year":"1984","unstructured":"Temam, R.: Navier\u2013Stokes equations. North-Holland, Amsterdam (1984)"},{"key":"556_CR31","first-page":"281","volume":"7","author":"J Wang","year":"2010","unstructured":"Wang, J., Wang, Y., Ye, X.: A new finite volume method for the stokes problems. Int. J. Numer. Anal. Mod. 7, 281\u2013302 (2010)","journal-title":"Int. J. Numer. Anal. Mod."},{"key":"556_CR32","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1002\/num.1021","volume":"5","author":"X Ye","year":"2001","unstructured":"Ye, X.: On the relationship between finite volume and finite element methods applied to the Stokes equations. Numer. Methods Partial Diff. Equ. 5, 440\u2013453 (2001)","journal-title":"Numer. Methods Partial Diff. Equ."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-013-0556-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-013-0556-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-013-0556-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,13]],"date-time":"2019-07-13T21:48:30Z","timestamp":1563054510000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-013-0556-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,5,17]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,1]]}},"alternative-id":["556"],"URL":"https:\/\/doi.org\/10.1007\/s00211-013-0556-2","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,5,17]]}}}