{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T18:31:39Z","timestamp":1773945099693,"version":"3.50.1"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2016,2,23]],"date-time":"2016-02-23T00:00:00Z","timestamp":1456185600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2016,12]]},"DOI":"10.1007\/s00211-015-0787-5","type":"journal-article","created":{"date-parts":[[2016,2,23]],"date-time":"2016-02-23T04:59:05Z","timestamp":1456203545000},"page":"783-822","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["A stable numerical method for the dynamics of fluidic membranes"],"prefix":"10.1007","volume":"134","author":[{"given":"John W.","family":"Barrett","sequence":"first","affiliation":[]},{"given":"Harald","family":"Garcke","sequence":"additional","affiliation":[]},{"given":"Robert","family":"N\u00fcrnberg","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,2,23]]},"reference":[{"key":"787_CR1","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.jcp.2014.08.016","volume":"277","author":"S Aland","year":"2014","unstructured":"Aland, S., Egerer, S., Lowengrub, J., Voigt, A.: Diffuse interface models of locally inextensible vesicles in a viscous fluid. J. Comput. Phys. 277, 32\u201347 (2014)","journal-title":"J. Comput. Phys."},{"key":"787_CR2","doi-asserted-by":"crossref","first-page":"031,915","DOI":"10.1103\/PhysRevE.79.031915","volume":"79","author":"M Arroyo","year":"2009","unstructured":"Arroyo, M., DeSimone, A.: Relaxation dynamics of fluid membranes. Phys. Rev. E 79, 031,915 (2009)","journal-title":"Phys. Rev. E"},{"key":"787_CR3","unstructured":"Arroyo, M., DeSimone, A., Heltai, L.: The role of membrane viscosity in the dynamics of fluid membranes (2010). arxiv.org\/abs\/1007.4934"},{"key":"787_CR4","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/PL00005443","volume":"88","author":"E B\u00e4nsch","year":"2001","unstructured":"B\u00e4nsch, E.: Finite element discretization of the Navier-Stokes equations with a free capillary surface. Numer. Math. 88, 203\u2013235 (2001)","journal-title":"Numer. Math."},{"key":"787_CR5","doi-asserted-by":"crossref","first-page":"4281","DOI":"10.1016\/j.jcp.2007.11.023","volume":"227","author":"JW Barrett","year":"2008","unstructured":"Barrett, J.W., Garcke, H., N\u00fcrnberg, R.: On the parametric finite element approximation of evolving hypersurfaces in $${\\mathbb{R}}^3$$ R 3 . J. Comput. Phys. 227, 4281\u20134307 (2008)","journal-title":"J. Comput. Phys."},{"key":"787_CR6","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1137\/070700231","volume":"31","author":"JW Barrett","year":"2008","unstructured":"Barrett, J.W., Garcke, H., N\u00fcrnberg, R.: Parametric approximation of Willmore flow and related geometric evolution equations. SIAM J. Sci. Comput. 31, 225\u2013253 (2008)","journal-title":"SIAM J. Sci. Comput."},{"key":"787_CR7","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1007\/s00211-011-0416-x","volume":"120","author":"JW Barrett","year":"2012","unstructured":"Barrett, J.W., Garcke, H., N\u00fcrnberg, R.: Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves. Numer. Math. 120, 489\u2013542 (2012)","journal-title":"Numer. Math."},{"key":"787_CR8","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1016\/j.cma.2013.09.023","volume":"267","author":"JW Barrett","year":"2013","unstructured":"Barrett, J.W., Garcke, H., N\u00fcrnberg, R.: Eliminating spurious velocities with a stable approximation of viscous incompressible two-phase Stokes flow. Comput. Methods Appl. Mech. Eng. 267, 511\u2013530 (2013)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"787_CR9","first-page":"421","volume":"49","author":"JW Barrett","year":"2015","unstructured":"Barrett, J.W., Garcke, H., N\u00fcrnberg, R.: On the stable numerical approximation of two-phase flow with insoluble surfactant. M2AN Math. Model. Numer. Anal. 49, 421\u2013458 (2015)","journal-title":"M2AN Math. Model. Numer. Anal."},{"key":"787_CR10","doi-asserted-by":"crossref","first-page":"1829","DOI":"10.4310\/CMS.2015.v13.n7.a9","volume":"13","author":"JW Barrett","year":"2015","unstructured":"Barrett, J.W., Garcke, H., N\u00fcrnberg, R.: Stable numerical approximation of two-phase flow with a Boussinesq-Scriven surface fluid. Commun. Math. Sci. 13, 1829\u20131874 (2015)","journal-title":"Commun. Math. Sci."},{"key":"787_CR11","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1007\/s10915-014-9885-2","volume":"63","author":"JW Barrett","year":"2015","unstructured":"Barrett, J.W., Garcke, H., N\u00fcrnberg, R.: A stable parametric finite element discretization of two-phase Navier-Stokes flow. J. Sci. Comput. 63, 78\u2013117 (2015)","journal-title":"J. Sci. Comput."},{"key":"787_CR12","doi-asserted-by":"crossref","first-page":"3171","DOI":"10.1016\/j.jcp.2009.12.036","volume":"229","author":"A Bonito","year":"2010","unstructured":"Bonito, A., Nochetto, R.H., Pauletti, M.S.: Parametric FEM for geometric biomembranes. J. Comput. Phys. 229, 3171\u20133188 (2010)","journal-title":"J. Comput. Phys."},{"key":"787_CR13","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1051\/mmnp\/20116502","volume":"6","author":"A Bonito","year":"2011","unstructured":"Bonito, A., Nochetto, R.H., Pauletti, M.S.: Dynamics of biomembranes: effect of the bulk fluid. Math. Model. Nat. Phenom. 6, 25\u201343 (2011)","journal-title":"Math. Model. Nat. Phenom."},{"key":"787_CR14","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1016\/j.cagd.2004.02.004","volume":"21","author":"U Clarenz","year":"2004","unstructured":"Clarenz, U., Diewald, U., Dziuk, G., Rumpf, M., Rusu, R.: A finite element method for surface restoration with smooth boundary conditions. Comput. Aided Geom. Design 21, 427\u2013445 (2004)","journal-title":"Comput. Aided Geom. Design"},{"key":"787_CR15","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1090\/S0025-5718-08-02176-5","volume":"78","author":"K Deckelnick","year":"2009","unstructured":"Deckelnick, K., Dziuk, G.: Error analysis for the elastic flow of parametrized curves. Math. Comput. 78, 645\u2013671 (2009)","journal-title":"Math. Comput."},{"key":"787_CR16","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1017\/S0962492904000224","volume":"14","author":"K Deckelnick","year":"2005","unstructured":"Deckelnick, K., Dziuk, G., Elliott, C.M.: Computation of geometric partial differential equations and mean curvature flow. Acta Numer. 14, 139\u2013232 (2005)","journal-title":"Acta Numer."},{"key":"787_CR17","doi-asserted-by":"crossref","first-page":"551","DOI":"10.4171\/IFB\/245","volume":"12","author":"K Deckelnick","year":"2010","unstructured":"Deckelnick, K., Schieweck, F.: Error analysis for the approximation of axisymmetric Willmore flow by $$C^1$$ C 1 -finite elements. Interfac. Free Bound. 12, 551\u2013574 (2010)","journal-title":"Interfac. Free Bound."},{"key":"787_CR18","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/s00211-008-0179-1","volume":"111","author":"G Dziuk","year":"2008","unstructured":"Dziuk, G.: Computational parametric Willmore flow. Numer. Math. 111, 55\u201380 (2008)","journal-title":"Numer. Math."},{"key":"787_CR19","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1017\/S0962492913000056","volume":"22","author":"G Dziuk","year":"2013","unstructured":"Dziuk, G., Elliott, C.M.: Finite element methods for surface PDEs. Acta Numer. 22, 289\u2013396 (2013)","journal-title":"Acta Numer."},{"key":"787_CR20","doi-asserted-by":"crossref","first-page":"6585","DOI":"10.1016\/j.jcp.2010.05.014","volume":"229","author":"CM Elliott","year":"2010","unstructured":"Elliott, C.M., Stinner, B.: Modeling and computation of two phase geometric biomembranes using surface finite elements. J. Comput. Phys. 229, 6585\u20136612 (2010)","journal-title":"J. Comput. Phys."},{"key":"787_CR21","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/s00791-012-0172-1","volume":"14","author":"T Franke","year":"2011","unstructured":"Franke, T., Hoppe, R.H.W., Linsenmann, C., Schmid, L., Willbold, C., Wixforth, A.: Numerical simulation of the motion of red blood cells and vesicles in microfluidic flows. Comput. Vis. Sci. 14, 167\u2013180 (2011)","journal-title":"Comput. Vis. Sci."},{"key":"787_CR22","first-page":"116","volume":"10","author":"M Franken","year":"2013","unstructured":"Franken, M., Rumpf, M., Wirth, B.: A phase field based PDE constrained optimization approach to time discrete Willmore flow. Int. J. Numer. Anal. Model. 10, 116\u2013138 (2013)","journal-title":"Int. J. Numer. Anal. Model."},{"key":"787_CR23","doi-asserted-by":"crossref","first-page":"670","DOI":"10.1016\/j.jcp.2013.10.018","volume":"257","author":"WF Hu","year":"2014","unstructured":"Hu, W.F., Kim, Y., Lai, M.C.: An immersed boundary method for simulating the dynamics of three-dimensional axisymmetric vesicles in Navier-Stokes flows. J. Comput. Phys. 257, 670\u2013686 (2014)","journal-title":"J. Comput. Phys."},{"key":"787_CR24","doi-asserted-by":"crossref","first-page":"051,907","DOI":"10.1103\/PhysRevE.76.051907","volume":"76","author":"D Jamet","year":"2007","unstructured":"Jamet, D., Misbah, C.: Towards a thermodynamically consistent picture of the phase-field model of vesicles: local membrane incompressibility. Phys. Rev. E 76, 051,907 (2007)","journal-title":"Phys. Rev. E"},{"key":"787_CR25","unstructured":"K\u00f6hne, M., Lengeler, D.: Local well-posedness for relaxational fluid vesicle dynamics (2015). arXiv:1512.02941"},{"key":"787_CR26","doi-asserted-by":"crossref","first-page":"9008","DOI":"10.1039\/C3SM51645H","volume":"9","author":"T Kr\u00fcger","year":"2013","unstructured":"Kr\u00fcger, T., Gross, M., Raabe, D., Varnik, F.: Crossover from tumbling to tank-treading-like motion in dense simulated suspensions of red blood cells. Soft Matter 9, 9008\u20139015 (2013)","journal-title":"Soft Matter"},{"key":"787_CR27","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1016\/j.jcp.2013.12.032","volume":"263","author":"A Laadhari","year":"2014","unstructured":"Laadhari, A., Saramito, P., Misbah, C.: Computing the dynamics of biomembranes by combining conservative level set and adaptive finite element methods. J. Comput. Phys. 263, 328\u2013352 (2014)","journal-title":"J. Comput. Phys."},{"key":"787_CR28","unstructured":"Lengeler, D.: On a Stokes-type system arising in fluid vesicle dynamics (2015). arxiv.org\/abs\/1506.08991"},{"key":"787_CR29","doi-asserted-by":"crossref","first-page":"89","DOI":"10.4171\/IFB\/54","volume":"4","author":"UF Mayer","year":"2002","unstructured":"Mayer, U.F., Simonett, G.: A numerical scheme for axisymmetric solutions of curvature-driven free boundary problems, with applications to the Willmore flow. Interfac. Free Bound. 4, 89\u2013109 (2002)","journal-title":"Interfac. Free Bound."},{"key":"787_CR30","doi-asserted-by":"crossref","first-page":"6039","DOI":"10.1073\/pnas.0811484106","volume":"106","author":"JL McWhirter","year":"2009","unstructured":"McWhirter, J.L., Noguchi, H., Gompper, G.: Flow-induced clustering and alignment of vesicles and red blood cells in microcapillaries. Proc. Natl. Acad. Sci. USA 106, 6039\u20136043 (2009)","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"787_CR31","doi-asserted-by":"crossref","first-page":"1768","DOI":"10.1137\/120885553","volume":"73","author":"M Mercker","year":"2013","unstructured":"Mercker, M., Marciniak-Czochra, A., Richter, T., Hartmann, D.: Modeling and computing of deformation dynamics of inhomogeneous biological surfaces. SIAM J. Appl. Math. 73, 1768\u20131792 (2013)","journal-title":"SIAM J. Appl. Math."},{"key":"787_CR32","doi-asserted-by":"crossref","first-page":"A1384","DOI":"10.1137\/130927668","volume":"36","author":"K Mikula","year":"2014","unstructured":"Mikula, K., Reme\u0161\u00edkov\u00e1, M., Sarkoci, P., \u0160ev\u010dovi\u010d, D.: Manifold evolution with tangential redistribution of points. SIAM J. Sci. Comput. 36, A1384\u2013A1414 (2014)","journal-title":"SIAM J. Sci. Comput."},{"key":"787_CR33","doi-asserted-by":"crossref","first-page":"011,932","DOI":"10.1103\/PhysRevE.86.011932","volume":"86","author":"M Rahimi","year":"2012","unstructured":"Rahimi, M., Arroyo, M.: Shape dynamics, lipid hydrodynamics, and the complex viscoelasticity of bilayer membranes. Phys. Rev. E 86, 011,932 (2012)","journal-title":"Phys. Rev. E"},{"key":"787_CR34","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1016\/j.jcp.2015.06.010","volume":"298","author":"DS Rodrigues","year":"2015","unstructured":"Rodrigues, D.S., Ausas, R.F., Mut, F., Buscaglia, G.C.: A semi-implicit finite element method for viscous lipid membranes. J. Comput. Phys. 298, 565\u2013584 (2015)","journal-title":"J. Comput. Phys."},{"key":"787_CR35","doi-asserted-by":"crossref","first-page":"8192","DOI":"10.1016\/j.jcp.2011.07.019","volume":"230","author":"D Salac","year":"2011","unstructured":"Salac, D., Miksis, M.: A level set projection model of lipid vesicles in general flows. J. Comput. Phys. 230, 8192\u20138215 (2011)","journal-title":"J. Comput. Phys."},{"key":"787_CR36","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1017\/jfm.2012.380","volume":"711","author":"D Salac","year":"2012","unstructured":"Salac, D., Miksis, M.J.: Reynolds number effects on lipid vesicles. J. Fluid Mech. 711, 122\u2013146 (2012)","journal-title":"J. Fluid Mech."},{"key":"787_CR37","volume-title":"Design of Adaptive Finite Element Software: The Finite Element Toolbox ALBERTA, Lecture Notes in Computational Science and Engineering","author":"A Schmidt","year":"2005","unstructured":"Schmidt, A., Siebert, K.G.: Design of Adaptive Finite Element Software: The Finite Element Toolbox ALBERTA, Lecture Notes in Computational Science and Engineering, vol. 42. Springer, Berlin (2005)"},{"key":"787_CR38","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/0009-2509(60)87003-0","volume":"12","author":"LE Scriven","year":"1960","unstructured":"Scriven, L.E.: Dynamics of a fluid interface: equation of motion for Newtonian surface fluids. Chem. Eng. Sci. 12, 98\u2013108 (1960)","journal-title":"Chem. Eng. Sci."},{"key":"787_CR39","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1080\/00018739700101488","volume":"46","author":"U Seifert","year":"1997","unstructured":"Seifert, U.: Configurations of fluid membranes and vesicles. Adv. Phys. 46, 13\u2013137 (1997)","journal-title":"Adv. Phys."},{"key":"787_CR40","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1002\/fld.3939","volume":"76","author":"L Shi","year":"2014","unstructured":"Shi, L., Pan, T.W., Glowinski, R.: Three-dimensional numerical simulation of red blood cell motion in Poiseuille flows. Internat. J. Numer. Methods Fluids 76, 397\u2013415 (2014)","journal-title":"Internat. J. Numer. Methods Fluids"},{"key":"787_CR41","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1142\/S0218202512500492","volume":"23","author":"L Beir\u00e3o da Veiga","year":"2013","unstructured":"Beir\u00e3o da Veiga, L., Brezzi, F., Cangiani, A., Manzini, G., Marini, L.D., Russo, A.: Basic principles of virtual element methods. Math. Models Methods Appl. Sci. 23, 199\u2013214 (2013)","journal-title":"Math. Models Methods Appl. Sci."},{"key":"787_CR42","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1209\/epl\/i1996-00353-8","volume":"33","author":"W Wintz","year":"1996","unstructured":"Wintz, W., D\u00f6bereiner, H.G., Seifert, U.: Starfish vesicles. Europhys. Lett. 33, 403\u2013408 (1996)","journal-title":"Europhys. Lett."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-015-0787-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-015-0787-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-015-0787-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-015-0787-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,26]],"date-time":"2019-03-26T19:14:36Z","timestamp":1553627676000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-015-0787-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,23]]},"references-count":42,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2016,12]]}},"alternative-id":["787"],"URL":"https:\/\/doi.org\/10.1007\/s00211-015-0787-5","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,2,23]]}}}