{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T10:42:48Z","timestamp":1777459368565,"version":"3.51.4"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2017,5,27]],"date-time":"2017-05-27T00:00:00Z","timestamp":1495843200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2018,2]]},"DOI":"10.1007\/s10915-017-0458-z","type":"journal-article","created":{"date-parts":[[2017,5,27]],"date-time":"2017-05-27T05:45:15Z","timestamp":1495863915000},"page":"631-639","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Convergence Analysis in the Maximum Norm of the Numerical Gradient of the Shortley\u2013Weller Method"],"prefix":"10.1007","volume":"74","author":[{"given":"Jiwon","family":"Seo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Seung-yeal","family":"Ha","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chohong","family":"Min","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,5,27]]},"reference":[{"issue":"3","key":"458_CR1","first-page":"523","volume":"7","author":"LA Caffarelli","year":"1980","unstructured":"Caffarelli, L.A., Gilardi, G.: Monotonicity of the free boundary in the two-dimensional dam problem. Annali della Scuola Normale Superiore di Pisa-Classe di Scienze 7(3), 523\u2013537 (1980)","journal-title":"Annali della Scuola Normale Superiore di Pisa-Classe di Scienze"},{"issue":"2","key":"458_CR2","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1006\/jcph.1997.5716","volume":"135","author":"AJ Chorin","year":"1997","unstructured":"Chorin, A.J.: A numerical method for solving incompressible viscous flow problems. J. Comput. Phys. 135(2), 118\u2013125 (1997)","journal-title":"J. Comput. Phys."},{"key":"458_CR3","doi-asserted-by":"crossref","DOI":"10.1017\/9781139171984","volume-title":"Introduction to Numerical Linear Algebra and Optimisation. Cambridge Texts in Applied Mathematics","author":"PG Ciarlet","year":"1989","unstructured":"Ciarlet, P.G., Miara, B., Thomas, J.M.: Introduction to Numerical Linear Algebra and Optimisation. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge (1989)"},{"key":"458_CR4","volume-title":"Variational principles and free-boundary problems","author":"A Friedman","year":"2010","unstructured":"Friedman, A.: Variational principles and free-boundary problems. Courier Corporation, North Chelmsford (2010)"},{"key":"458_CR5","first-page":"3245","volume":"231","author":"F Gibou","year":"2012","unstructured":"Gibou, F., Min, C.: Efficient symmetric positive definite second-order accurate monolithic solver for fluid\/solid interactions. J. Comput. Phys. 231, 3245\u20133263 (2012)","journal-title":"J. Comput. Phys."},{"key":"458_CR6","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1007\/BF01931691","volume":"18","author":"I Gustafsson","year":"1978","unstructured":"Gustafsson, I.: A class of first order factorization methods. BIT 18, 142\u2013156 (1978)","journal-title":"BIT"},{"issue":"3","key":"458_CR7","doi-asserted-by":"crossref","first-page":"2182","DOI":"10.1063\/1.1761178","volume":"8","author":"FH Harlow","year":"1965","unstructured":"Harlow, F.H., Welch, J.E.: Numerical calculation of time-dependent viscous incompressible flow of fluid with a free surface. Phys. Fluids 8(3), 2182\u20132189 (1965)","journal-title":"Phys. Fluids"},{"key":"458_CR8","volume-title":"A First Course in the Numerical Analysis of Differential Equations. Cambridge Texts in Applied Mathematics","author":"A Iserles","year":"1996","unstructured":"Iserles, A.: A First Course in the Numerical Analysis of Differential Equations. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge (1996)"},{"issue":"5","key":"458_CR9","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1016\/j.apnum.2007.02.007","volume":"58","author":"Z-C Li","year":"2008","unstructured":"Li, Z.-C., Hu, H.-Y., Wang, S., Fang, Q.: Superconvergence of solution derivatives of the shortley-weller difference approximation to poisson\u2019s equation with singularities on polygonal domains. Appl. Numer. Math. 58(5), 689\u2013704 (2008)","journal-title":"Appl. Numer. Math."},{"issue":"2","key":"458_CR10","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1007\/s10915-009-9299-8","volume":"41","author":"YT Ng","year":"2009","unstructured":"Ng, Y.T., Chen, H., Min, C., Gibou, F.: Guidelines for poisson solvers on irregular domains with dirichlet boundary conditions using the ghost fluid method. J. Sci. Comput. 41(2), 300\u2013320 (2009)","journal-title":"J. Sci. Comput."},{"key":"458_CR11","doi-asserted-by":"crossref","unstructured":"Peskin, C.S.: Flow patterns around heart valves. In: Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics, pp. 214\u2013221. Springer (1973)","DOI":"10.1007\/BFb0112697"},{"issue":"5","key":"458_CR12","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1063\/1.1710426","volume":"9","author":"GH Shortley","year":"1938","unstructured":"Shortley, G.H., Weller, R.: The numerical solution of Laplace\u2019s equation. J. Appl. Phys. 9(5), 334\u2013348 (1938)","journal-title":"J. Appl. Phys."},{"key":"458_CR13","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898717938","volume-title":"Finite Difference Schemes and Partial Differential Equations","author":"JC Strikwerda","year":"2004","unstructured":"Strikwerda, J.C.: Finite Difference Schemes and Partial Differential Equations. SIAM, New Delhi (2004)"},{"key":"458_CR14","unstructured":"Weynans, L.: A proof in the finite-difference spirit of the superconvergence of the gradient for the Shortley\u2013Weller method. Ph.D. thesis, INRIA Bordeaux (2015)"},{"issue":"2","key":"458_CR15","doi-asserted-by":"crossref","first-page":"658","DOI":"10.1006\/jcph.2001.6847","volume":"172","author":"D Xiu","year":"2001","unstructured":"Xiu, D., Karniadakis, G.E.: A semi-Lagrangian high-order method for Navier\u2013Stokes equations. J. Comput. Phys. 172(2), 658\u2013684 (2001)","journal-title":"J. Comput. Phys."},{"key":"458_CR16","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1016\/j.jcp.2014.09.009","volume":"280","author":"G Yoon","year":"2015","unstructured":"Yoon, G., Min, C.: Analyses on the finite difference method by Gibou, et al. for poisson equation. J. Comput. Phys. 280, 184\u2013194 (2015)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"458_CR17","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1007\/s10915-015-0096-2","volume":"67","author":"G Yoon","year":"2016","unstructured":"Yoon, G., Min, C.: Convergence analysis of the standard central finite difference method for Poisson equation. J. Sci. Comput. 67(2), 602\u2013617 (2016)","journal-title":"J. Sci. Comput."},{"key":"458_CR18","unstructured":"Yoon, G., Min, C., Kim, S.: A stable and convergent method for hodge decomposition of fluid-solid interaction. (2016). arXiv:1610.03195"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-017-0458-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0458-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0458-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,25]],"date-time":"2019-09-25T01:32:17Z","timestamp":1569375137000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-017-0458-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,27]]},"references-count":18,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,2]]}},"alternative-id":["458"],"URL":"https:\/\/doi.org\/10.1007\/s10915-017-0458-z","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,5,27]]}}}