{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:39:51Z","timestamp":1740123591024,"version":"3.37.3"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,5,11]],"date-time":"2021-05-11T00:00:00Z","timestamp":1620691200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,5,11]],"date-time":"2021-05-11T00:00:00Z","timestamp":1620691200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100008736","name":"Fondo de Fomento al Desarrollo Cient\u00edfico y Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["3190204","11180193"],"award-info":[{"award-number":["3190204","11180193"]}],"id":[{"id":"10.13039\/501100008736","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["11200529"],"award-info":[{"award-number":["11200529"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2021,6]]},"DOI":"10.1007\/s10915-021-01496-x","type":"journal-article","created":{"date-parts":[[2021,5,11]],"date-time":"2021-05-11T20:02:48Z","timestamp":1620763368000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Error Estimates for FEM Discretizations of the Navier\u2013Stokes Equations with Dirac Measures"],"prefix":"10.1007","volume":"87","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7929-9572","authenticated-orcid":false,"given":"Felipe","family":"Lepe","sequence":"first","affiliation":[]},{"given":"Enrique","family":"Ot\u00e1rola","sequence":"additional","affiliation":[]},{"given":"Daniel","family":"Quero","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,5,11]]},"reference":[{"key":"1496_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4939-6985-2","volume-title":"Divergence operator and related inequalities. springerbriefs in mathematics","author":"G Acosta","year":"2017","unstructured":"Acosta, G., Dur\u00e1n, R.G.: Divergence operator and related inequalities. springerbriefs in mathematics. Springer, New York (2017). https:\/\/doi.org\/10.1007\/978-1-4939-6985-2"},{"key":"1496_CR2","volume-title":"Sobolev Spaces Pure and Applied Mathematics","author":"RA Adams","year":"2003","unstructured":"Adams, R.A., Fournier, J.J.F.: Sobolev Spaces Pure and Applied Mathematics. Elsevier\/Academic Press, Amsterdam (2003)"},{"issue":"1","key":"1496_CR3","doi-asserted-by":"publisher","first-page":"228","DOI":"10.1137\/S0036142994264092","volume":"34","author":"M Ainsworth","year":"1997","unstructured":"Ainsworth, M., Oden, J.T.: A posteriori error estimators for the Stokes and Oseen equations. SIAM J. Numer. Anal. 34(1), 228\u2013245 (1997). https:\/\/doi.org\/10.1137\/S0036142994264092","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"1496_CR4","doi-asserted-by":"publisher","first-page":"A1860","DOI":"10.1137\/19M1292436","volume":"42","author":"A Allendes","year":"2020","unstructured":"Allendes, A., Ot\u00e1rola, E., Salgado, A.J.: A posteriori error estimates for the stationary Navier-Stokes equations with Dirac measures. SIAM J. Sci. Comput. 42(3), A1860\u2013A1884 (2020). https:\/\/doi.org\/10.1137\/19M1292436","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"1496_CR5","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/s00211-006-0041-2","volume":"105","author":"R Araya","year":"2006","unstructured":"Araya, R., Behrens, E., Rodr\u00edguez, R.: A posteriori error estimates for elliptic problems with Dirac delta source terms. Numer. Math. 105(2), 193\u2013216 (2006). https:\/\/doi.org\/10.1007\/s00211-006-0041-2","journal-title":"Numer. Math."},{"issue":"6","key":"1496_CR6","doi-asserted-by":"publisher","first-page":"1237","DOI":"10.1137\/0725070","volume":"25","author":"C Bernardi","year":"1988","unstructured":"Bernardi, C., Canuto, C., Maday, Y.: Generalized inf-sup conditions for Chebyshev spectral approximation of the Stokes problem. SIAM J. Numer. Anal. 25(6), 1237\u20131271 (1988). https:\/\/doi.org\/10.1137\/0725070","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"1496_CR7","doi-asserted-by":"publisher","first-page":"1328","DOI":"10.1137\/18M1185582","volume":"57","author":"E Casas","year":"2019","unstructured":"Casas, E., Kunisch, K.: Optimal control of the two-dimensional stationary Navier-Stokes equations with measure valued controls. SIAM J. Control Optim. 57(2), 1328\u20131354 (2019). https:\/\/doi.org\/10.1137\/18M1185582","journal-title":"SIAM J. Control Optim."},{"key":"1496_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4355-5","author":"A Ern","year":"2004","unstructured":"Ern, A., Guermond, J.L.: Theory and practice of finite elements. Appl. Math. Sci. (2004). https:\/\/doi.org\/10.1007\/978-1-4757-4355-5","journal-title":"Appl. Math. Sci."},{"key":"1496_CR9","doi-asserted-by":"publisher","unstructured":"Fuica, F., Lepe, F., Ot\u00e1rola, E., Quero, D.: A posteriori error estimates in $${\\bf W}^{1,p} \\times {L}^p$$ spaces for the Stokes system with Dirac measures. Comput. Math. Appl. 94, 47\u201359 (2021). https:\/\/doi.org\/10.1016\/j.camwa.2021.04.017","DOI":"10.1016\/j.camwa.2021.04.017"},{"key":"1496_CR10","doi-asserted-by":"crossref","unstructured":"Fuica, F., Otarola, E., Quero, D.: Error estimates for optimal control problems involving the Stokes system and Dirac measures. Appl. Math, Optim (2020). https:\/\/doi.org\/10.1007\/s00245-020-09693-0","DOI":"10.1007\/s00245-020-09693-0"},{"key":"1496_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-09620-9","volume-title":"An introduction to the mathematical theory of the Navier-Stokes Springer Monographs in Mathematics. equations","author":"GP Galdi","year":"2011","unstructured":"Galdi, G.P.: An introduction to the mathematical theory of the Navier-Stokes Springer Monographs in Mathematics. equations, 2nd edn. Springer, New York (2011). https:\/\/doi.org\/10.1007\/978-0-387-09620-9. Steady-state problems","edition":"2"},{"issue":"4","key":"1496_CR12","doi-asserted-by":"publisher","first-page":"771","DOI":"10.1007\/s00211-015-0707-8","volume":"131","author":"V Girault","year":"2015","unstructured":"Girault, V., Nochetto, R.H., Scott, L.R.: Max-norm estimates for Stokes and Navier-Stokes approximations in convex polyhedra. Numer. Math. 131(4), 771\u2013822 (2015). https:\/\/doi.org\/10.1007\/s00211-015-0707-8","journal-title":"Numer. Math."},{"key":"1496_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2004.09.017","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. (2005). https:\/\/doi.org\/10.1016\/j.matpur.2004.09.017","journal-title":"J. Math. Pures Appl."},{"key":"1496_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61623-5","volume-title":"Finite Element Methods for Navier-Stokes Equations, Springer Series in Computational Mathematics","author":"V Girault","year":"1986","unstructured":"Girault, V., Raviart, P.A.: Finite Element Methods for Navier-Stokes Equations, Springer Series in Computational Mathematics, vol. 5. Springer, Berlin (1986). https:\/\/doi.org\/10.1007\/978-3-642-61623-5. Theory and algorithms"},{"issue":"3","key":"1496_CR15","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1016\/j.crme.2014.09.008","volume":"343","author":"L Lacouture","year":"2015","unstructured":"Lacouture, L.: A numerical method to solve the Stokes problem with a punctual force in source term. Comptes Rendus Mecanique 343(3), 187\u2013191 (2015). https:\/\/doi.org\/10.1016\/j.crme.2014.09.008","journal-title":"Comptes Rendus Mecanique"},{"key":"1496_CR16","unstructured":"Lions, P.L.: Mathematical topics in fluid mechanics. Vol. 1, Oxford Lecture Series in Mathematics and its Applications, vol.\u00a03. The Clarendon Press, Oxford University Press, New York (1996). Incompressible models, Oxford Science Publications"},{"key":"1496_CR17","unstructured":"Mitrea, M., Wright, M.: Boundary value problems for the Stokes system in arbitrary Lipschitz domains. Ast\u00e9risque (344), viii+241 (2012)"},{"key":"1496_CR18","doi-asserted-by":"publisher","first-page":"105933, 7","DOI":"10.1016\/j.aml.2019.06.004","volume":"99","author":"E Ot\u00e1rola","year":"2020","unstructured":"Ot\u00e1rola, E., Salgado, A.J.: A weighted setting for the stationary Navier Stokes equations under singular forcing. Appl. Math. Lett. 99, 105933, 7 (2020). https:\/\/doi.org\/10.1016\/j.aml.2019.06.004","journal-title":"Appl. Math. Lett."},{"key":"1496_CR19","doi-asserted-by":"publisher","unstructured":"Tartar, L.: An introduction to Navier-Stokes equation and oceanography, Lecture Notes of the Unione Matematica Italiana, vol.\u00a01. Springer, Berlin; UMI, Bologna (2006). https:\/\/doi.org\/10.1007\/3-540-36545-1","DOI":"10.1007\/3-540-36545-1"},{"key":"1496_CR20","doi-asserted-by":"publisher","unstructured":"Temam, R.: Navier-Stokes equations. AMS Chelsea Publishing, Providence, RI (2001). https:\/\/doi.org\/10.1090\/chel\/343. Theory and numerical analysis, Reprint of the 1984 edition","DOI":"10.1090\/chel\/343"},{"key":"1496_CR21","doi-asserted-by":"crossref","unstructured":"Tsai, T.P.: Lectures on Navier-Stokes equations, Graduate Studies in Mathematics, vol. 192. American Mathematical Society, Providence, RI (2018)","DOI":"10.1090\/gsm\/192"},{"issue":"3","key":"1496_CR22","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1007\/BF01390056","volume":"55","author":"R Verf\u00fcrth","year":"1989","unstructured":"Verf\u00fcrth, R.: A posteriori error estimators for the Stokes equations. Numer. Math. 55(3), 309\u2013325 (1989). https:\/\/doi.org\/10.1007\/BF01390056","journal-title":"Numer. Math."},{"issue":"4","key":"1496_CR23","doi-asserted-by":"publisher","first-page":"641","DOI":"10.1007\/s002110050381","volume":"80","author":"R Verf\u00fcrth","year":"1998","unstructured":"Verf\u00fcrth, R.: A posteriori error estimators for convection-diffusion equations. Numer. Math. 80(4), 641\u2013663 (1998). https:\/\/doi.org\/10.1007\/s002110050381","journal-title":"Numer. Math."},{"key":"1496_CR24","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199679423.001.0001","volume-title":"A Posteriori Error Estimation Techniques for Finite Element Methods. Numerical Mathematics and Scientific Computation.","author":"R Verf\u00fcrth","year":"2013","unstructured":"Verf\u00fcrth, R.: A Posteriori Error Estimation Techniques for Finite Element Methods. Numerical Mathematics and Scientific Computation. Oxford University Press, Oxford (2013)"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-021-01496-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-021-01496-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-021-01496-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,24]],"date-time":"2021-05-24T18:32:11Z","timestamp":1621881131000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-021-01496-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,11]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["1496"],"URL":"https:\/\/doi.org\/10.1007\/s10915-021-01496-x","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2021,5,11]]},"assertion":[{"value":"2 September 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 January 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 April 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 May 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"97"}}