{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:45:35Z","timestamp":1740123935993,"version":"3.37.3"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2020,7,31]],"date-time":"2020-07-31T00:00:00Z","timestamp":1596153600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,7,31]],"date-time":"2020-07-31T00:00:00Z","timestamp":1596153600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["415673"],"award-info":[{"award-number":["415673"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2020,10]]},"DOI":"10.1007\/s10444-020-09798-8","type":"journal-article","created":{"date-parts":[[2020,7,31]],"date-time":"2020-07-31T10:04:10Z","timestamp":1596189850000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Difference potentials method for models with dynamic boundary conditions and bulk-surface problems"],"prefix":"10.1007","volume":"46","author":[{"given":"Yekaterina","family":"Epshteyn","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1583-2446","authenticated-orcid":false,"given":"Qing","family":"Xia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,7,31]]},"reference":[{"volume-title":"Handbook of mathematical functions with formulas, graphs, and mathematical tables","year":"1992","key":"9798_CR1","unstructured":"Abramowitz, M., Stegun, I.A. (eds.): Handbook of mathematical functions with formulas, graphs, and mathematical tables. Dover Publications, Inc., New York (1992). Reprint of the 1972 edition"},{"key":"9798_CR2","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/j.apnum.2014.08.002","volume":"93","author":"J Albright","year":"2015","unstructured":"Albright, J., Epshteyn, Y., Steffen, K.R.: High-order accurate difference potentials methods for parabolic problems. Appl. Numer. Math. 93, 87\u2013106 (2015). https:\/\/doi.org\/10.1016\/j.apnum.2014.08.002","journal-title":"Appl. Numer. Math."},{"issue":"4","key":"9798_CR3","doi-asserted-by":"publisher","first-page":"985","DOI":"10.4310\/CMS.2017.v15.n4.a4","volume":"15","author":"J Albright","year":"2017","unstructured":"Albright, J., Epshteyn, Y., Xia, Q.: High-order accurate methods based on difference potentials for 2D parabolic interface models. Commun. Math. Sci. 15(4), 985\u20131019 (2017). https:\/\/doi.org\/10.4310\/CMS.2017.v15.n4.a4","journal-title":"Commun. Math. Sci."},{"issue":"4","key":"9798_CR4","doi-asserted-by":"publisher","first-page":"777","DOI":"10.4171\/RLM\/785","volume":"28","author":"P Bardsley","year":"2017","unstructured":"Bardsley, P., Barmak, K., Eggeling, E., Epshteyn, Y., Kinderlehrer, D., Ta\u2019asan, S.: Towards a gradient flow for microstructure. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 28(4), 777\u2013805 (2017). https:\/\/doi.org\/10.4171\/RLM\/785","journal-title":"Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl."},{"key":"9798_CR5","doi-asserted-by":"publisher","first-page":"530","DOI":"10.1016\/j.jcp.2015.05.029","volume":"297","author":"JW Barrett","year":"2015","unstructured":"Barrett, J.W., Garcke, H., N\u00fcrnberg, R.: Stable finite element approximations of two-phase flow with soluble surfactant. J. Comput. Phys. 297, 530\u2013564 (2015). https:\/\/doi.org\/10.1016\/j.jcp.2015.05.029","journal-title":"J. Comput. Phys."},{"issue":"2","key":"9798_CR6","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/s00211-015-0744-3","volume":"133","author":"E Burman","year":"2015","unstructured":"Burman, E., Hansbo, P., Larson, M.G., Zahedi, S.: Cut finite element methods for coupled bulk\u2013surface problems. Numer. Math. 133(2), 203\u2013231 (2015). https:\/\/doi.org\/10.1007\/s00211-015-0744-3","journal-title":"Numer. Math."},{"issue":"part A","key":"9798_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jcp.2013.10.003","volume":"257","author":"KY Chen","year":"2014","unstructured":"Chen, K.Y., Lai, M.C.: A conservative scheme for solving coupled surface-bulk convection-diffusion equations with an application to interfacial flows with soluble surfactant. J. Comput. Phys. 257(part A), 1\u201318 (2014). https:\/\/doi.org\/10.1016\/j.jcp.2013.10.003","journal-title":"J. Comput. Phys."},{"key":"9798_CR8","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1016\/j.cma.2015.03.025","volume":"291","author":"AY Chernyshenko","year":"2015","unstructured":"Chernyshenko, A.Y., Olshanskii, M.A.: An adaptive octree finite element method for PDEs posed on surfaces. Comput. Methods Appl. Mech. Engrg. 291, 146\u2013172 (2015). https:\/\/doi.org\/10.1016\/j.cma.2015.03.025","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"9798_CR9","doi-asserted-by":"publisher","first-page":"516","DOI":"10.1016\/j.jcp.2017.09.064","volume":"352","author":"AY Chernyshenko","year":"2018","unstructured":"Chernyshenko, A.Y., Olshanskii, M.A., Vassilevski, Y.V.: A hybrid finite volume\u2013finite element method for bulk-surface coupled problems. J. Comput. Phys. 352, 516\u2013533 (2018). https:\/\/doi.org\/10.1016\/j.jcp.2017.09.064","journal-title":"J. Comput. Phys."},{"issue":"1","key":"9798_CR10","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1007\/s00233-008-9068-2","volume":"77","author":"GM Coclite","year":"2008","unstructured":"Coclite, G.M., Favini, A., Goldstein, G.R., Goldstein, J.A., Romanelli, S.: Continuous dependence on the boundary conditions for the Wentzell Laplacian. Semigroup Forum 77(1), 101\u2013108 (2008). https:\/\/doi.org\/10.1007\/s00233-008-9068-2","journal-title":"Semigroup Forum"},{"issue":"9","key":"9798_CR11","doi-asserted-by":"publisher","first-page":"2595","DOI":"10.1016\/j.jde.2007.12.006","volume":"245","author":"GM Coclite","year":"2008","unstructured":"Coclite, G.M., Goldstein, G.R., Goldstein, J.A.: Stability estimates for parabolic problems with Wentzell boundary conditions. J. Differential Equations 245(9), 2595\u20132626 (2008). https:\/\/doi.org\/10.1016\/j.jde.2007.12.006","journal-title":"J. Differential Equations"},{"key":"9798_CR12","doi-asserted-by":"crossref","unstructured":"Cusseddu, D., Edelstein-Keshet, L., Mackenzie, J., Portet, S., Madzvamuse, A.: A coupled bulk-surface model for cell polarisation. J. Theor. Biol. (2018)","DOI":"10.1016\/j.jtbi.2018.09.008"},{"key":"9798_CR13","doi-asserted-by":"publisher","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). https:\/\/doi.org\/10.1017\/S0962492913000056","journal-title":"Acta Numer."},{"issue":"2","key":"9798_CR14","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1093\/imanum\/drs022","volume":"33","author":"CM Elliott","year":"2013","unstructured":"Elliott, C.M., Ranner, T.: Finite element analysis for a coupled bulk-surface partial differential equation. IMA J. Numer. Anal. 33(2), 377\u2013402 (2013). https:\/\/doi.org\/10.1093\/imanum\/drs022","journal-title":"IMA J. Numer. Anal."},{"issue":"1","key":"9798_CR15","doi-asserted-by":"publisher","first-page":"360","DOI":"10.1137\/15m1050811","volume":"49","author":"CM Elliott","year":"2017","unstructured":"Elliott, C.M., Ranner, T., Venkataraman, C.: Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-Ligand dynamics. SIAM J. Math. Anal. 49(1), 360\u2013397 (2017). https:\/\/doi.org\/10.1137\/15m1050811","journal-title":"SIAM J. Math. Anal."},{"issue":"1","key":"9798_CR16","doi-asserted-by":"publisher","first-page":"360","DOI":"10.1137\/15M1050811","volume":"49","author":"CM Elliott","year":"2017","unstructured":"Elliott, C.M., Ranner, T., Venkataraman, C.: Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics. SIAM J. Math. Anal. 49(1), 360\u2013397 (2017). https:\/\/doi.org\/10.1137\/15M1050811","journal-title":"SIAM J. Math. Anal."},{"issue":"4","key":"9798_CR17","doi-asserted-by":"publisher","first-page":"723","DOI":"10.4310\/CMS.2014.v12.n4.a7","volume":"12","author":"Y Epshteyn","year":"2014","unstructured":"Epshteyn, Y.: Algorithms composition approach based on difference potentials method for parabolic problems. Commun. Math. Sci. 12(4), 723\u2013755 (2014). https:\/\/doi.org\/10.4310\/CMS.2014.v12.n4.a7","journal-title":"Commun. Math. Sci."},{"issue":"1","key":"9798_CR18","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1007\/s10915-019-00928-z","volume":"80","author":"Y Epshteyn","year":"2019","unstructured":"Epshteyn, Y., Xia, Q.: Efficient numerical algorithms based on difference potentials for chemotaxis systems in 3D. J. Sci. Comput. 80(1), 26\u201359 (2019). https:\/\/doi.org\/10.1007\/s10915-019-00928-z","journal-title":"J. Sci. Comput."},{"issue":"5","key":"9798_CR19","doi-asserted-by":"publisher","first-page":"1303","DOI":"10.1051\/m2an\/2015013","volume":"49","author":"S Gross","year":"2015","unstructured":"Gross, S., Olshanskii, M.A., Reusken, A.: A trace finite element method for a class of coupled bulk-interface transport problems. ESAIM Math. Model. Numer. Anal. 49(5), 1303\u20131330 (2015). https:\/\/doi.org\/10.1051\/m2an\/2015013","journal-title":"ESAIM Math. Model. Numer. Anal."},{"key":"9798_CR20","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1016\/j.cma.2016.04.012","volume":"307","author":"P Hansbo","year":"2016","unstructured":"Hansbo, P., Larson, M.G., Zahedi, S.: A cut finite element method for coupled bulk-surface problems on time-dependent domains. Comput. Methods Appl. Mech. Eng. 307, 96\u2013116 (2016). https:\/\/doi.org\/10.1016\/j.cma.2016.04.012","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"1","key":"9798_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1093\/imanum\/drw015","volume":"37","author":"B Kova\u0307cs","year":"2016","unstructured":"Kova\u0307cs, B., Lubich, C.: Numerical analysis of parabolic problems with dynamic boundary conditions. IMA J. Numer. Anal. 37(1), 1\u201339 (2016). https:\/\/doi.org\/10.1093\/imanum\/drw015","journal-title":"IMA J. Numer. Anal."},{"key":"9798_CR22","doi-asserted-by":"crossref","unstructured":"Liu, C., Wu, H.: An energetic variational approach for the cahn-hilliard equation with dynamic boundary conditions: Derivation and analysis. Arch. Ration. Mech. Anal. (2019)","DOI":"10.1007\/s00205-019-01356-x"},{"issue":"2","key":"9798_CR23","doi-asserted-by":"publisher","first-page":"812","DOI":"10.1007\/s10915-017-0637-y","volume":"76","author":"G Ludvigsson","year":"2018","unstructured":"Ludvigsson, G., Steffen, K.R., Sticko, S., Wang, S., Xia, Q., Epshteyn, Y., Kreiss, G.: High-order numerical methods for 2d parabolic problems in single and composite domains. J. Sci. Comput. 76(2), 812\u2013847 (2018). https:\/\/doi.org\/10.1007\/s10915-017-0637-y","journal-title":"J. Sci. Comput."},{"key":"9798_CR24","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1016\/j.finel.2015.09.002","volume":"108","author":"A Madzvamuse","year":"2016","unstructured":"Madzvamuse, A., Chung, A.H.: The bulk-surface finite element method for reaction\u2013diffusion systems on stationary volumes. Finite Elem. Anal. Des. 108, 9\u201321 (2016). https:\/\/doi.org\/10.1016\/j.finel.2015.09.002","journal-title":"Finite Elem. Anal. Des."},{"key":"9798_CR25","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/j.apnum.2017.02.013","volume":"118","author":"S Magura","year":"2017","unstructured":"Magura, S., Petropavlovsky, S., Tsynkov, S., Turkel, E.: High-order numerical solution of the Helmholtz equation for domains with reentrant corners. Appl. Numer. Math. 118, 87\u2013116 (2017). https:\/\/doi.org\/10.1016\/j.apnum.2017.02.013","journal-title":"Appl. Numer. Math."},{"key":"9798_CR26","doi-asserted-by":"crossref","unstructured":"Massing, A.: A cut discontinuous galerkin method for coupled bulk-surface problems. In: Bordas, S.P.A., Burman, E., Larson, M.G., Olshanskii, M.A. (eds.) Geometrically Unfitted Finite Element Methods and Applications, pp 259\u2013279. Springer International Publishing, Cham (2017)","DOI":"10.1007\/978-3-319-71431-8_8"},{"key":"9798_CR27","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1016\/j.jcp.2018.09.040","volume":"376","author":"M Medvinsky","year":"2019","unstructured":"Medvinsky, M., Tsynkov, S., Turkel, E.: Direct implementation of high order BGT artificial boundary conditions. J. Comput. Phys. 376, 98\u2013128 (2019). https:\/\/doi.org\/10.1016\/j.jcp.2018.09.040","journal-title":"J. Comput. Phys."},{"issue":"2","key":"9798_CR28","doi-asserted-by":"publisher","first-page":"1271","DOI":"10.1016\/j.jcp.2007.05.025","volume":"226","author":"IL Novak","year":"2007","unstructured":"Novak, I.L., Gao, F., Choi, Y.S., Resasco, D., Schaff, J.C., Slepchenko, B.M.: Diffusion on a curved surface coupled to diffusion in the volume: Application to cell biology. J. Comput. Phys. 226(2), 1271\u20131290 (2007). https:\/\/doi.org\/10.1016\/j.jcp.2007.05.025","journal-title":"J. Comput. Phys."},{"issue":"3","key":"9798_CR29","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1007\/s00211-009-0260-4","volume":"114","author":"MA Olshanskii","year":"2010","unstructured":"Olshanskii, M.A., Reusken, A.: A finite element method for surface PDEs: matrix properties. Numer. Math. 114(3), 491\u2013520 (2010). https:\/\/doi.org\/10.1007\/s00211-009-0260-4","journal-title":"Numer. Math."},{"key":"9798_CR30","doi-asserted-by":"crossref","unstructured":"Olshanskii, M.A., Reusken, A.: Trace finite element methods for PDEs on surfaces. In: Geometrically Unfitted Finite Element Methods and Applications, Lect. Notes Comput. Sci. Eng., vol. 121, pp 211\u2013258. Springer, Cham (2017)","DOI":"10.1007\/978-3-319-71431-8_7"},{"key":"9798_CR31","doi-asserted-by":"publisher","first-page":"294","DOI":"10.1016\/j.jcp.2018.03.039","volume":"365","author":"S Petropavlovsky","year":"2018","unstructured":"Petropavlovsky, S., Tsynkov, S., Turkel, E.: A method of boundary equations for unsteady hyperbolic problems in 3D. J. Comput. Phys. 365, 294\u2013323 (2018). https:\/\/doi.org\/10.1016\/j.jcp.2018.03.039","journal-title":"J. Comput. Phys."},{"key":"9798_CR32","doi-asserted-by":"publisher","unstructured":"Ryaben\u2019kii, V.S.: Method of difference potentials and its applications. In: Springer Series in Computational Mathematics. Translated from the 2001 Russian original by Nikolai K. Kulman, vol. 30. Springer-Verlag, Berlin (2002), https:\/\/doi.org\/10.1007\/978-3-642-56344-7","DOI":"10.1007\/978-3-642-56344-7"},{"issue":"10","key":"9798_CR33","doi-asserted-by":"publisher","first-page":"1768","DOI":"10.1134\/s0965542506100137","volume":"46","author":"VS Ryaben\u2019kii","year":"2006","unstructured":"Ryaben\u2019kii, V.S., Turchaninov, V.I., Epshteyn, Y.Y.: Algorithm composition scheme for problems in composite domains based on the difference potential method. Comput. Math. Math. Phys. 46(10), 1768\u20131784 (2006). https:\/\/doi.org\/10.1134\/s0965542506100137","journal-title":"Comput. Math. Math. Phys."},{"issue":"4","key":"9798_CR34","doi-asserted-by":"publisher","first-page":"2143","DOI":"10.1016\/j.jde.2010.12.012","volume":"250","author":"JL Va\u0307zquez","year":"2011","unstructured":"Va\u0307zquez, J.L., Vitillaro, E.: Heat equation with dynamical boundary conditions of reactive\u2013diffusive type. J. Differ. Equ. 250(4), 2143\u20132161 (2011). https:\/\/doi.org\/10.1016\/j.jde.2010.12.012","journal-title":"J. Differ. Equ."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-020-09798-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10444-020-09798-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-020-09798-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,31]],"date-time":"2021-07-31T00:41:25Z","timestamp":1627692085000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10444-020-09798-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,31]]},"references-count":34,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2020,10]]}},"alternative-id":["9798"],"URL":"https:\/\/doi.org\/10.1007\/s10444-020-09798-8","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"type":"print","value":"1019-7168"},{"type":"electronic","value":"1572-9044"}],"subject":[],"published":{"date-parts":[[2020,7,31]]},"assertion":[{"value":"17 April 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 May 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 July 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"67"}}