{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T12:02:23Z","timestamp":1759838543888},"reference-count":53,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T00:00:00Z","timestamp":1178841600000},"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":[[2007,8,7]]},"DOI":"10.1007\/s00211-007-0085-y","type":"journal-article","created":{"date-parts":[[2007,5,10]],"date-time":"2007-05-10T11:42:59Z","timestamp":1178797379000},"page":"213-255","source":"Crossref","is-referenced-by-count":18,"title":["Mathematical and numerical analysis of a simplified time-dependent viscoelastic flow"],"prefix":"10.1007","volume":"107","author":[{"given":"Andrea","family":"Bonito","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Philippe","family":"Cl\u00e9ment","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marco","family":"Picasso","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2007,5,11]]},"reference":[{"key":"85_CR1","volume-title":"Sobolev Spaces","author":"R.A. Adams","year":"1970","unstructured":"Adams R.A. (1970). Sobolev Spaces. Academic, INC. London"},{"issue":"1\u20132","key":"85_CR2","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1017\/S0308210500024598","volume":"115","author":"S.B. Angenent","year":"1990","unstructured":"Angenent S.B. (1990). Nonlinear analytic semiflows. Proc. R. Soc. Edinburgh Sect. A 115(1\u20132): 91\u2013107","journal-title":"Proc. R. Soc. Edinburgh Sect. A"},{"key":"85_CR3","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/S0377-0257(98)00122-0","volume":"79","author":"F.P.T. Baaijens","year":"1998","unstructured":"Baaijens F.P.T. (1998). Mixed finite element methods for viscoelastic flow analysis: a review. J. Non Newtonian Fluid Mech. 79: 361\u2013385","journal-title":"J. Non Newtonian Fluid Mech."},{"issue":"1","key":"85_CR4","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/BF01385845","volume":"63","author":"J. Baranger","year":"1992","unstructured":"Baranger J. and Sandri D. (1992). Finite element approximation of viscoelastic fluid flow: existence of approximate solutions and error bounds. I. Discontinuous constraints. Numer. Math. 63(1): 13\u201327","journal-title":"Numer. Math."},{"issue":"1\u20134","key":"85_CR5","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/0045-7825(94)00763-D","volume":"125","author":"J. Baranger","year":"1995","unstructured":"Baranger J. and Wardi S. (1995). Numerical analysis of a FEM for a transient viscoelastic flow. Comput. Methods Appl. Mech. Engrg. 125(1\u20134): 171\u2013185","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"85_CR6","volume-title":"Dynamics of polymeric liquids, vol. 1 and 2","author":"R. Bird","year":"1987","unstructured":"Bird R., Curtiss C., Armstrong R. and Hassager O. (1987). Dynamics of polymeric liquids, vol. 1 and 2. Wiley, New York"},{"key":"85_CR7","unstructured":"Bonito, A.: Analysis and numerical simulation of viscoelastic flows : deterministic and stochastic models. PhD thesis, D\u00e9partement de Math\u00e9matiques, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne (2006)"},{"issue":"4","key":"85_CR8","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1051\/m2an:2006030","volume":"40","author":"A. Bonito","year":"2006","unstructured":"Bonito A., Cl\u00e9ment Ph. and Picasso M. (2006). Finite element analysis of a simplified stochastic Hookean dumbbells model arising from viscoelastic flows. M2AN Math. Model. Numer. Anal. 40(4): 785\u2013814","journal-title":"M2AN Math. Model. Numer. Anal."},{"issue":"3","key":"85_CR9","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1007\/s00028-006-0251-1","volume":"6","author":"A. Bonito","year":"2006","unstructured":"Bonito A., Cl\u00e9ment Ph. and Picasso M. (2006). Mathematical analysis of a simplified Hookean dumbbells model arising from viscoelastic flows. J. Evol. Equ. 6(3): 381\u2013398","journal-title":"J. Evol. Equ."},{"issue":"2","key":"85_CR10","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1016\/j.jcp.2005.11.013","volume":"215","author":"A. Bonito","year":"2006","unstructured":"Bonito A., Picasso M. and Laso M. (2006). Numerical simulation of 3d viscoelastic flows with complex free surfaces. J. Comput. Phys. 215(2): 691\u2013716","journal-title":"J. Comput. Phys."},{"issue":"29\u201330","key":"85_CR11","doi-asserted-by":"crossref","first-page":"3893","DOI":"10.1016\/S0045-7825(00)00307-8","volume":"190","author":"J. Bonvin","year":"2001","unstructured":"Bonvin J., Picasso M. and Stenberg R. (2001). GLS and EVSS methods for a three-field Stokes problem arising from viscoelastic flows. Comput. Methods Appl. Mech. Engrg. 190(29\u201330): 3893\u20133914","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"issue":"1","key":"85_CR12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01395985","volume":"36","author":"F. Brezzi","year":"1980\/81","unstructured":"Brezzi, F., Rappaz, J., Raviart, P.-A.: Finite-dimensional approximation of nonlinear problems. I. Branches of nonsingular solutions. Numer. Math. 36(1), 1\u201325 (1980\/81)","journal-title":"Numer. Math."},{"issue":"1","key":"85_CR13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01396184","volume":"37","author":"F. Brezzi","year":"1981","unstructured":"Brezzi F., Rappaz J. and Raviart P.-A. (1981). Finite-dimensional approximation of nonlinear problems. II. Limit points. Numer. Math. 37(1): 1\u201328","journal-title":"Numer. Math."},{"key":"85_CR14","doi-asserted-by":"crossref","unstructured":"Buffoni, B., Toland, J.: Analytic theory of global bifurcation. Princeton Series in Applied Mathematics. Princeton University Press, Princeton (2003) An introduction","DOI":"10.1515\/9781400884339"},{"key":"85_CR15","doi-asserted-by":"crossref","unstructured":"Caloz, G., Rappaz J.: Numerical analysis for nonlinear and bifurcation problems. In: Handbook of numerical analysis, vol. V, Handb. Numer. Anal., V, pp. 487\u2013637. North-Holland, Amsterdam (1997)","DOI":"10.1016\/S1570-8659(97)80004-X"},{"key":"85_CR16","volume-title":"Calcul diff\u00e9rentiel","author":"H. Cartan","year":"1967","unstructured":"Cartan H. (1967). Calcul diff\u00e9rentiel. Hermann, Paris"},{"key":"85_CR17","unstructured":"Ciarlet, P.G., Lions, J.-L.: (eds.) Handbook of numerical analysis. Vol. II. Handbook of Numerical Analysis, II. North-Holland, Amsterdam (1991) Finite element methods. Part 1"},{"key":"85_CR18","unstructured":"Da Prato, G., Sinestrari, E.: Differential operators with nondense domain. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 14(2), 285\u2013344 (1988), 1987"},{"issue":"4","key":"85_CR19","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/BF01762539","volume":"138","author":"G. Di Blasio","year":"1984","unstructured":"Di Blasio G. (1984). Linear parabolic evolution equations in L p -spaces. Ann. Mat. Pura Appl. 138(4): 55\u2013104","journal-title":"Ann. Mat. Pura Appl."},{"key":"85_CR20","doi-asserted-by":"crossref","unstructured":"Dore, G.: L p regularity for abstract differential equations. In: Functional analysis and related topics, 1991 (Kyoto), vol. 1540 of Lecture Notes in Math., pp. 25\u201338. Springer, Berlin (1993)","DOI":"10.1007\/BFb0085472"},{"issue":"2","key":"85_CR21","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/BF01163654","volume":"196","author":"G. Dore","year":"1987","unstructured":"Dore G. and Venni A. (1987). On the closedness of the sum of two closed operators. Math. Z. 196(2): 189\u2013201","journal-title":"Math. Z."},{"issue":"2","key":"85_CR22","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1002\/num.10086","volume":"20","author":"V.J. Ervin","year":"2004","unstructured":"Ervin V.J. and Heuer N. (2004). Approximation of time-dependent, viscoelastic fluid flow: Crank-Nicolson, finite element approximation. Numer. Methods Partial Diff. Eqn. 20(2): 248\u2013283","journal-title":"Numer. Methods Partial Diff. Eqn."},{"issue":"2","key":"85_CR23","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1137\/S003614290241177X","volume":"41","author":"V.J. Ervin","year":"2003","unstructured":"Ervin V.J. and Miles W.W. (2003). Approximation of time-dependent viscoelastic fluid flow: SUPG approximation. SIAM J. Numer. Anal. 41(2): 457\u2013486.(electronic)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"85_CR24","first-page":"93","volume":"7","author":"M. Farhloul","year":"2003","unstructured":"Farhloul M. and Zine A.M. (2003). A new mixed finite element method for viscoelastic fluid flows. Int. J. Pure Appl. Math. 7(1): 93\u2013115","journal-title":"Int. J. Pure Appl. Math."},{"key":"85_CR25","doi-asserted-by":"crossref","unstructured":"Fern\u00e1ndez-Cara, E., Guill\u00e9n, F., Ortega, R.R.: Mathematical modeling and analysis of viscoelastic fluids of the Oldroyd kind. In: Handbook of numerical analysis, vol. VIII, Handb. Numer. Anal., VIII, pp. 543\u2013661. North-Holland, Amsterdam (2002)","DOI":"10.1016\/S1570-8659(02)08005-5"},{"issue":"1","key":"85_CR26","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/S0045-7825(99)00292-3","volume":"189","author":"A. Fortin","year":"2000","unstructured":"Fortin A., Gu\u00e9nette R. and Pierre R. (2000). On the discrete EVSS method. Comput. Methods Appl. Mech. Engrg. 189(1): 121\u2013139","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"issue":"3","key":"85_CR27","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1016\/0045-7825(89)90073-X","volume":"73","author":"M. Fortin","year":"1989","unstructured":"Fortin M. and Pierre R. (1989). On the convergence of the mixed method of Crochet and Marchal for viscoelastic flows. Comput. Methods Appl. Mech. Engrg. 73(3): 341\u2013350","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"issue":"3","key":"85_CR28","first-page":"685","volume":"24","author":"D. Fujiwara","year":"1977","unstructured":"Fujiwara D. and Morimoto H. (1977). An L r -theorem of the Helmholtz decomposition of vector fields. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 24(3): 685\u2013700","journal-title":"J. Fac. Sci. Univ. Tokyo Sect. IA Math."},{"key":"85_CR29","unstructured":"Galdi, G.P.: An introduction to the mathematical theory of the Navier-Stokes equations. vol. I, volume 38 of Springer Tracts in Natural Philosophy. Springer-Verlag, New York, (1994) Linearized steady problems"},{"issue":"1","key":"85_CR30","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s00208-004-0573-7","volume":"331","author":"G.P. Galdi","year":"2005","unstructured":"Galdi G.P., Simader C.G. and Sohr H. (2005). A class of solutions to stationary Stokes and Navier-Stokes equations with boundary data in W \u22121\/q,q . Math. Ann. 331(1): 41\u201374","journal-title":"Math. Ann."},{"issue":"1\u20132","key":"85_CR31","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/0377-0257(82)85016-7","volume":"11","author":"H. Giesekus","year":"1982","unstructured":"Giesekus H. (1982). A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility. J. Non Newtonian Fluid Mech. 11(1\u20132): 69\u2013109","journal-title":"J. Non Newtonian Fluid Mech."},{"issue":"3","key":"85_CR32","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/BF01214869","volume":"178","author":"Y. Giga","year":"1981","unstructured":"Giga Y. (1981). Analyticity of the semigroup generated by the Stokes operator in L r spaces. Math. Z. 178(3): 297\u2013329","journal-title":"Math. Z."},{"key":"85_CR33","doi-asserted-by":"crossref","unstructured":"Glowinski, R.: Finite element methods for incompressible viscous flow. In Handbook of numerical analysis, Vol. IX, Handb. Numer. Anal., IX, pp. 3\u20131176. North-Holland, Amsterdam (2003)","DOI":"10.1016\/S1570-8659(03)09003-3"},{"issue":"9","key":"85_CR34","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1016\/0362-546X(90)90097-Z","volume":"15","author":"C. Guillop\u00e9","year":"1990","unstructured":"Guillop\u00e9 C. and Saut J.-C. (1990). Existence results for the flow of viscoelastic fluids with a differential constitutive law. Nonlinear Anal. 15(9): 849\u2013869","journal-title":"Nonlinear Anal."},{"key":"85_CR35","unstructured":"Keunings, R.: Micro-marco methods for the multi-scale simulation of viscoelastic flow using molecular models of kinetic theory. Rheol. Rev., pp. 67\u201398 (2004)"},{"issue":"2","key":"85_CR36","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1142\/S0252959900000170","volume":"21","author":"P.L. Lions","year":"2000","unstructured":"Lions P.L. and Masmoudi N. (2000). Global solutions for some Oldroyd models of non-Newtonian flows. Chinese Ann. Math. Ser. B 21(2): 131\u2013146","journal-title":"Chinese Ann. Math. Ser. B"},{"key":"85_CR37","volume-title":"Analytic semigroups and optimal regularity in parabolic problems. Progress in Nonlinear Differential Equations and their Applications 16.","author":"A. Lunardi","year":"1995","unstructured":"Lunardi A. (1995). Analytic semigroups and optimal regularity in parabolic problems. Progress in Nonlinear Differential Equations and their Applications 16.. Birkh\u00e4user Verlag, Basel"},{"issue":"42","key":"85_CR38","doi-asserted-by":"crossref","first-page":"5603","DOI":"10.1016\/S0045-7825(01)00186-4","volume":"190","author":"A. Machmoum","year":"2001","unstructured":"Machmoum A. and Esselaoui D. (2001). Finite element approximation of viscoelastic fluid flow using characteristics method. Comput. Methods Appl. Mech. Engrg. 190(42): 5603\u20135618","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"issue":"2","key":"85_CR39","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s002110050167","volume":"72","author":"K. Najib","year":"1995","unstructured":"Najib K. and Sandri D. (1995). On a decoupled algorithm for solving a finite element problem for the approximation of viscoelastic fluid flow. Numer. Math. 72(2): 223\u2013238","journal-title":"Numer. Math."},{"key":"85_CR40","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-58290-5","volume-title":"Stochastic processes in polymeric fluids","author":"H.C. \u00d6ttinger","year":"1996","unstructured":"\u00d6ttinger H.C. (1996). Stochastic processes in polymeric fluids. Springer, Berlin"},{"key":"85_CR41","doi-asserted-by":"crossref","DOI":"10.1142\/p160","volume-title":"Computational rheology","author":"R.G. Owens","year":"2002","unstructured":"Owens R.G. and Phillips T.N. (2002). Computational rheology. Imperial College Press, London"},{"issue":"4","key":"85_CR42","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1016\/0377-0257(77)80021-9","volume":"2","author":"N. Phan-Thien","year":"1977","unstructured":"Phan-Thien N. and Tanner R.I. (1977). A new constitutive equation derived from network theory. J. Non Newtonian Fluid Mech. 2(4): 353\u2013365","journal-title":"J. Non Newtonian Fluid Mech."},{"issue":"5","key":"85_CR43","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1051\/m2an:2001140","volume":"35","author":"M. Picasso","year":"2001","unstructured":"Picasso M. and Rappaz J. (2001). Existence, a priori and a posteriori error estimates for a nonlinear three-field problem arising from Oldroyd-B viscoelastic flows. M2AN Math. Model. Numer. Anal. 35(5): 879\u2013897","journal-title":"M2AN Math. Model. Numer. Anal."},{"key":"85_CR44","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-8570-6","volume-title":"Evolutionary integral equations and applications, volume 87 of Monographs in Mathematics","author":"J. Pr\u00fcss","year":"1993","unstructured":"Pr\u00fcss J. (1993). Evolutionary integral equations and applications, volume 87 of Monographs in Mathematics. Birkh\u00e4user Verlag, Basel"},{"issue":"4","key":"85_CR45","first-page":"T40","volume":"68","author":"M. Renardy","year":"1988","unstructured":"Renardy M. (1988). Existence of slow steady flows of viscoelastic fluids of integral type. Z. Angew. Math. Mech. 68(4): T40\u2013T44","journal-title":"Z. Angew. Math. Mech."},{"issue":"7","key":"85_CR46","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1051\/m2an\/1993270708171","volume":"27","author":"D. Sandri","year":"1993","unstructured":"Sandri D. (1993). Analyse d\u2019une formulation \u00e0 trois champs du probl\u00e8me de Stokes. RAIRO Mod\u00e9l. Math. Anal. Num\u00e9r. 27(7): 817\u2013841","journal-title":"RAIRO Mod\u00e9l. Math. Anal. Num\u00e9r."},{"issue":"2","key":"85_CR47","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1137\/0731019","volume":"31","author":"D. Sandri","year":"1994","unstructured":"Sandri D. (1994). Finite element approximation of viscoelastic fluid flow: existence of approximate solutions and error bounds. Continuous approximation of the stress. SIAM J. Numer. Anal. 31(2): 362\u2013377","journal-title":"SIAM J. Numer. Anal."},{"key":"85_CR48","doi-asserted-by":"crossref","unstructured":"Simader, C.G., Sohr, H.: A new approach to the Helmholtz decomposition and the Neumann problem in L q -spaces for bounded and exterior domains. In: Mathematical problems relating to the Navier\u2013Stokes equation. vol. 11 of Ser. Adv. Math. Appl. Sci. pp. 1\u201335. World Scientific Publishing, River Edge (1992)","DOI":"10.1142\/9789814503594_0001"},{"issue":"1","key":"85_CR49","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/0022-247X(85)90353-1","volume":"107","author":"E. Sinestrari","year":"1985","unstructured":"Sinestrari E. (1985). On the abstract Cauchy problem of parabolic type in spaces of continuous functions. J. Math. Anal. Appl. 107(1): 16\u201366","journal-title":"J. Math. Anal. Appl."},{"key":"85_CR50","first-page":"52","volume":"157","author":"P.E. Sobolevski\u012d","year":"1964","unstructured":"Sobolevski\u012d P.E. (1964). Coerciveness inequalities for abstract parabolic equations. Dokl. Akad. Nauk SSSR 157: 52\u201355","journal-title":"Dokl. Akad. Nauk SSSR"},{"issue":"6","key":"85_CR51","first-page":"1271","volume":"225","author":"P.E. Sobolevski\u012d","year":"1975","unstructured":"Sobolevski\u012d P.E. (1975). Fractional powers of coercively positive sums of operators. Dokl. Akad. Nauk SSSR 225(6): 1271\u20131274","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"85_CR52","doi-asserted-by":"crossref","unstructured":"Solonnikov, V.A.: Estimates of the Solutions of a Nonstationary Linearized System of Navier\u2013Stokes Equations, pp. 214\u2013317. American Mathematical Society, Rhode island (1968)","DOI":"10.1090\/trans2\/075\/01"},{"key":"85_CR53","volume-title":"Functional analysis, volume 123 of Grundlehren der Mathematischen Wissenschaften (Fundamental Principles of Mathematical Sciences)","author":"K. Yosida","year":"1980","unstructured":"Yosida K. (1980). Functional analysis, volume 123 of Grundlehren der Mathematischen Wissenschaften (Fundamental Principles of Mathematical Sciences). Springer, Berlin"}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-007-0085-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-007-0085-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-007-0085-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T16:22:39Z","timestamp":1558628559000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-007-0085-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,5,11]]},"references-count":53,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2007,8,7]]}},"alternative-id":["85"],"URL":"https:\/\/doi.org\/10.1007\/s00211-007-0085-y","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,5,11]]}}}