{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T07:01:41Z","timestamp":1787382101550,"version":"build-2736575974"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2016,12,1]],"date-time":"2016-12-01T00:00:00Z","timestamp":1480550400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11601251"],"award-info":[{"award-number":["11601251"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shandong province higher educational science and technology program","award":["J16LI10"],"award-info":[{"award-number":["J16LI10"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2017,8]]},"DOI":"10.1007\/s10444-016-9505-9","type":"journal-article","created":{"date-parts":[[2016,12,1]],"date-time":"2016-12-01T13:38:24Z","timestamp":1480599504000},"page":"759-775","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Supercloseness of the SDFEM on Shishkin triangular meshes for problems with exponential layers"],"prefix":"10.1007","volume":"43","author":[{"given":"Jin","family":"Zhang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaowei","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2016,12,1]]},"reference":[{"issue":"6","key":"9505_CR1","doi-asserted-by":"crossref","first-page":"2294","DOI":"10.1137\/S003614290139874X","volume":"41","author":"RE Bank","year":"2003","unstructured":"Bank, R.E., Xu, J.: Asymptotically exact a posteriori error estimators, part I: Grids with superconvergence. SIAM J. Numer. Anal. 41(6), 2294\u20132312 (2003)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"9505_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0962492904000212","volume":"14","author":"M Benzi","year":"2005","unstructured":"Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numer. 14(1), 1\u2013137 (2005)","journal-title":"Acta Numer."},{"issue":"1","key":"9505_CR3","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/s10444-011-9228-x","volume":"38","author":"H Chen","year":"2013","unstructured":"Chen, H., Lin, Q., Zhou, J., Wang, H.: Uniform error estimates for triangular finite element solutions of advection-diffusion equations. Adv Comput. Math. 38(1), 83\u2013100 (2013)","journal-title":"Adv Comput. Math."},{"issue":"278","key":"9505_CR4","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1090\/S0025-5718-2011-02526-3","volume":"81","author":"S Franz","year":"2012","unstructured":"Franz, S., Kellogg, R.B., Stynes, M.: Galerkin and streamline diffusion finite element methods on a Shishkin mesh for a convection-diffusion problem with corner singularities. Math. Comp. 81(278), 661\u2013685 (2012)","journal-title":"Math. Comp."},{"issue":"12","key":"9505_CR5","doi-asserted-by":"crossref","first-page":"1818","DOI":"10.1016\/j.apnum.2007.11.005","volume":"58","author":"S Franz","year":"2008","unstructured":"Franz, S., Lin\u00df, T., Roos, H.-G.: Superconvergence analysis of the SDFEM for elliptic problems with characteristic layers. Appl. Numer. Math. 58(12), 1818\u20131829 (2008)","journal-title":"Appl. Numer. Math."},{"issue":"1","key":"9505_CR6","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1093\/imanum\/17.1.29","volume":"17","author":"W Guo","year":"1997","unstructured":"Guo, W., Stynes, M.: Pointwise error estimates for a streamline diffusion scheme on a Shishkin mesh for a convection\u2013diffusion problem. IMA J. Numer Anal. 17(1), 29\u201359 (1997)","journal-title":"IMA J. Numer Anal."},{"key":"9505_CR7","unstructured":"Hughes, T.J.R., Brooks, A.: A multidimensional upwind scheme with no crosswind diffusion. In: Hughes, T.J.R. (ed.) Finite Element Methods for Convection Dominated Flows, volume AMD 34, pp. 19\u201335. Amer. Soc. Mech. Engrs (ASME)., New York (1979)"},{"key":"9505_CR8","unstructured":"Lin, Q., Yan, N., Zhou, A.: A Rectangle Test for Interpolated Finite Elements. In: Proceedings Systems Science and Engineering (Hong Kong, 1991), pp. 217\u2013229. Great Wall Culture Publishing, Whittier, CA (1991)"},{"issue":"2","key":"9505_CR9","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1006\/jmaa.2001.7550","volume":"261","author":"T Lin\u00df","year":"2001","unstructured":"Lin\u00df, T., Stynes, M.: Asymptotic analysis and Shishkin-type decomposition for an elliptic convection\u2013diffusion problem. J. Math. Anal. Appl. 261(2), 604\u2013632 (2001)","journal-title":"J. Math. Anal. Appl."},{"issue":"28","key":"9505_CR10","doi-asserted-by":"crossref","first-page":"3527","DOI":"10.1016\/S0045-7825(00)00271-1","volume":"190","author":"T Lin\u00df","year":"2001","unstructured":"Lin\u00df, T., Stynes, M.: Numerical methods on Shishkin meshes for linear convection\u2013diffusion problems. Comput. Methods Appl. Mech. Engrg. 190(28), 3527\u20133542 (2001)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"issue":"8","key":"9505_CR11","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1002\/zamm.200510264","volume":"86","author":"H-G Roos","year":"2006","unstructured":"Roos, H.-G.: Superconvergence on a hybrid mesh for singularly perturbed problems with exponential layers. ZAMM Z. Angew. Math. Mech. 86(8), 649\u2013655 (2006)","journal-title":"ZAMM Z. Angew. Math. Mech."},{"key":"9505_CR12","volume-title":"Robust Numerical Methods for Singularly Perturbed Differential Equations Volume 24 of Springer Series in Computational Mathematics","author":"H-G Roos","year":"2008","unstructured":"Roos, H.-G., Stynes, M., Tobiska, L.: Robust Numerical Methods for Singularly Perturbed Differential Equations Volume 24 of Springer Series in Computational Mathematics, second. Springer, Berlin (2008)","edition":"second"},{"issue":"3","key":"9505_CR13","doi-asserted-by":"crossref","first-page":"856","DOI":"10.1137\/0907058","volume":"7","author":"Y Saad","year":"1986","unstructured":"Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 7(3), 856\u2013869 (1986)","journal-title":"SIAM J. Sci. Statist. Comput."},{"key":"9505_CR14","volume-title":"Grid Approximation of Singularly Perturbed Elliptic and Parabolic Equations (In Russian). Second doctoral thesis","author":"GI Shishkin","year":"1990","unstructured":"Shishkin, G.I.: Grid Approximation of Singularly Perturbed Elliptic and Parabolic Equations (In Russian). Second doctoral thesis. Keldysh Institute, Moscow (1990)"},{"key":"9505_CR15","doi-asserted-by":"crossref","unstructured":"Stynes, M.: Steady-state convection-diffusion problems. Acta Numer. 14, 445\u2013508 (2005)","DOI":"10.1017\/S0962492904000261"},{"issue":"1","key":"9505_CR16","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1006\/jmaa.1997.5581","volume":"214","author":"M Stynes","year":"1997","unstructured":"Stynes, M., O\u2019Riordan, E.: A uniformly convergent G,alerkin method on a Shishkin mesh for a convection-diffusion problem. J. Math. Anal Appl. 214(1), 36\u201354 (1997)","journal-title":"J. Math. Anal Appl."},{"issue":"5","key":"9505_CR17","doi-asserted-by":"crossref","first-page":"1620","DOI":"10.1137\/S0036142902404728","volume":"41","author":"M Stynes","year":"2003","unstructured":"Stynes, M., Tobiska, L.: The SDFEM for a convection\u2013diffusion problem with a boundary layer: optimal error analysis and enhancement of accuracy. SIAM J. Numer. Anal. 41(5), 1620\u20131642 (2003)","journal-title":"SIAM J. Numer. Anal."},{"key":"9505_CR18","unstructured":"Stynes, M., Tobiska, L.: Using rectangular Q p elements in the SDFEM for a convection\u2013diffusion problem with a boundary layer. Appl. Numer. Math. 58(12), 1789\u20131802 (2008)"},{"issue":"4","key":"9505_CR19","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1007\/s00211-005-0598-1","volume":"100","author":"H Zarin","year":"2005","unstructured":"Zarin, H., Roos, H.-G.: Interior penalty discontinuous approximations of convection\u2013diffusion problems with parabolic layers. Numer. Math. 100(4), 735\u2013759 (2005)","journal-title":"Numer. Math."},{"key":"9505_CR20","unstructured":"Zhang, J., Liu, X.: Analysis of the SDFEM in a modified streamline diffusion norm for singularly perturbed convection diffusion problems. arXiv: 1603.02099 (2016)"},{"key":"9505_CR21","unstructured":"Zhang, J., Mei, L., Chen, Y.: Pointwise estimates of the SDFEM for convection\u2013diffusion problems with characteristic layers. Appl. Numer. Math. 64, 19\u201334 (2013)"},{"issue":"243","key":"9505_CR22","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.1090\/S0025-5718-03-01486-8","volume":"72","author":"Z Zhang","year":"2003","unstructured":"Zhang, Z.: Finite element superconvergence on Shishkin mesh for 2-D convection\u2013diffusion problems. Math. Comp. 72(243), 1147\u20131177 (2003)","journal-title":"Math. Comp."},{"key":"9505_CR23","unstructured":"Zhu, H., Zhang, Z.: Uniform convergence of the LDG method for a singularly perturbed problem with the exponential boundary layer. Math. Comp. 83(286), 635\u2013663 (2014)"}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-016-9505-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-016-9505-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-016-9505-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,16]],"date-time":"2019-09-16T01:15:47Z","timestamp":1568596547000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-016-9505-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,12,1]]},"references-count":23,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2017,8]]}},"alternative-id":["9505"],"URL":"https:\/\/doi.org\/10.1007\/s10444-016-9505-9","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,12,1]]}}}