{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:14:52Z","timestamp":1772295292901,"version":"3.50.1"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2013,10,26]],"date-time":"2013-10-26T00:00:00Z","timestamp":1382745600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2014,8]]},"DOI":"10.1007\/s10444-013-9327-y","type":"journal-article","created":{"date-parts":[[2013,10,25]],"date-time":"2013-10-25T16:41:46Z","timestamp":1382719306000},"page":"797-818","source":"Crossref","is-referenced-by-count":4,"title":["Robust a posteriori error estimates for conforming discretizations of a singularly perturbed reaction-diffusion problem on anisotropic meshes"],"prefix":"10.1007","volume":"40","author":[{"given":"Jikun","family":"Zhao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaochun","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,10,26]]},"reference":[{"key":"9327_CR1","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1023\/B:NUMA.0000005400.45852.f3","volume":"34","author":"M Afif","year":"2003","unstructured":"Afif, M., Bergam, A., Mghazli, Z., Verf\u00fcrth, R.: A posteriori estimators for the finite volume discretization of an elliptic equation. Numer. Algoritm. 34, 127\u2013136 (2003)","journal-title":"Numer. Algoritm."},{"key":"9327_CR2","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/s10915-010-9352-7","volume":"43","author":"M Afif","year":"2010","unstructured":"Afif, M., Amaziane, B., Kunert, G., Mghazli, Z.: A posteriori error estimation for a finite volume discretization on anisotropic meshes. J. Sci. Comput. 43, 183\u2013200 (2010)","journal-title":"J. Sci. Comput."},{"key":"9327_CR3","doi-asserted-by":"crossref","DOI":"10.1002\/9781118032824","volume-title":"A Posteriori Error Estimation in Finite Element Analysis","author":"M Ainsworth","year":"2000","unstructured":"Ainsworth, M., Oden, J.T.: A Posteriori Error Estimation in Finite Element Analysis. Wiley, New York (2000)"},{"key":"9327_CR4","unstructured":"Apel, T.: Anisotropic finite elements: local estimates and applications. Advances in Numercal Mathematics. Teubner (1999)"},{"key":"9327_CR5","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-3172-1","volume-title":"Mixed and Hybrid Finite Element Methods","author":"F Brezzi","year":"1991","unstructured":"Brezzi, F., Fortin, M.: Mixed and Hybrid Finite Element Methods. Springer, New York (1991)"},{"key":"9327_CR6","doi-asserted-by":"crossref","first-page":"867","DOI":"10.1051\/m2an\/2009012","volume":"43","author":"I Cheddadi","year":"2009","unstructured":"Cheddadi, I., Fu\u010d\u013ak, R., Prieto, M.I., Vohral\u013ak, M.: Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems. M2AN Math. Model. Numer. Anal. 43, 867\u2013888 (2009)","journal-title":"M2AN Math. Model. Numer. Anal."},{"key":"9327_CR7","unstructured":"Grosman, S.: The robustness of the hierarchical a posteriori error estimator for reaction-diffusion equation on anisotropic meshes, SFB393-Preprint 2, Technische Universit\u00e4t Chemnitz, SFB 393 (Germany) (2004)"},{"key":"9327_CR8","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1051\/m2an:2006010","volume":"40","author":"S Grosman","year":"2006","unstructured":"Grosman, S.: An equilibrated residual method with a computable error approximation for a singularly perturbed reaction-diffusion problem on anisotropic finite element meshes. M2AN Math. Model. Numer. Anal. 40, 239\u2013267 (2006)","journal-title":"M2AN Math. Model. Numer. Anal."},{"key":"9327_CR9","volume-title":"A posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes","author":"G Kunert","year":"1999","unstructured":"Kunert, G.: A posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes. Logos Verlag, Berlin (1999). Also PhD thesis, TU Chemnitz, http:\/\/archiv.tu-chemnitz.de\/pub\/1999\/0012\/index.html"},{"key":"9327_CR10","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1007\/s002110000170","volume":"86","author":"G Kunert","year":"2000","unstructured":"Kunert, G.: An a posteriori residual error estimator for the finite element method on anisotropic tetrahedral meshes. Numer. Math. 86, 471\u2013490 (2000)","journal-title":"Numer. Math."},{"key":"9327_CR11","doi-asserted-by":"crossref","unstructured":"Kunert, G.: A local problem error estimator for anisotropic tetrahedral finite element meshes. SIAM J. Numer. Anal. 39 (668\u2013689)","DOI":"10.1137\/S003614299935615X"},{"key":"9327_CR12","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1023\/A:1014248711347","volume":"15","author":"G Kunert","year":"2001","unstructured":"Kunert, G.: Robust a posteriori error estimation for a singularly perturbed reaction-diffusion equation on ainsotropic tetrahedral meshes. Adv. Comput. Math. 15, 237\u2013259 (2001)","journal-title":"Adv. Comput. Math."},{"key":"9327_CR13","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.1051\/m2an:2001149","volume":"35","author":"G Kunert","year":"2001","unstructured":"Kunert, G.: Robust local problem error estimation for a singularly perturbed problem on anisotropic finite element meshes. ESAIM: M2AN 35, 1079\u20131109 (2001)","journal-title":"ESAIM: M2AN"},{"key":"9327_CR14","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1093\/imanum\/drh009","volume":"25","author":"G Kunert","year":"2005","unstructured":"Kunert, G.: A posteriori H 1 $H^{1}$ error estimation for a singularly perturbed reaction diffusion problem on anisotopic meshes. IMA J. Numer. Anal. 25, 408\u2013428 (2005)","journal-title":"IMA J. Numer. Anal."},{"key":"9327_CR15","doi-asserted-by":"crossref","first-page":"1013","DOI":"10.1051\/m2an:2003065","volume":"37","author":"G Kunert","year":"2003","unstructured":"Kunert, G., Nicaise, S.: Zienkiewicz-Zhu error estimators on anisotropic tetrahedral and triangular finite element meshes. ESAIM: Math. Model. Numer. Anal. 37, 1013\u20131043 (2003)","journal-title":"ESAIM: Math. Model. Numer. Anal."},{"key":"9327_CR16","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/PL00005407","volume":"86","author":"G Kunert","year":"2000","unstructured":"Kunert, G., Verf\u00fcrth, R.: Edge residuals dominate a posteriori error estimates for linear finite element methods on anisotropic triangular and tetrahedral meshes. Numer. Math. 86, 283\u2013303 (2000)","journal-title":"Numer. Math."},{"key":"9327_CR17","first-page":"290","volume":"44","author":"JA Mackenzie","year":"1993","unstructured":"Mackenzie, J.A., Mayers, D.F., Mayfield, A.J.: Error estimates and mesh adaption for a cell vertex finite volume scheme. Notes Numer. Fluid Mech. 44, 290\u2013310 (1993)","journal-title":"Notes Numer. Fluid Mech."},{"key":"9327_CR18","doi-asserted-by":"crossref","DOI":"10.1515\/9783110203042","volume-title":"A posteriori estimates for partial differential equations, radon series on computational and applied mathematics,Vol. 4","author":"SI Repin","year":"2008","unstructured":"Repin, S.I.: A posteriori estimates for partial differential equations, radon series on computational and applied mathematics, Vol. 4. de Gruyter, Berlin (2008)"},{"key":"9327_CR19","doi-asserted-by":"crossref","DOI":"10.1016\/S1570-8659(05)80041-9","volume-title":"Mixed and Hybrid Methods","author":"JE Roberts","year":"1991","unstructured":"Roberts, J.E., Thomas, J.M.: Mixed and Hybrid Methods. North-Holland, Amsterdam (1991)"},{"key":"9327_CR20","volume-title":"A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques","author":"R Verf\u00fcrth","year":"1996","unstructured":"Verf\u00fcrth, R.: A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Teubner-Wiley, Stuttgart (1996)"},{"issue":"3","key":"9327_CR21","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/s002110050322","volume":"78","author":"R Verf\u00fcrth","year":"1998","unstructured":"Verf\u00fcrth, R.: Robust a posteriori error estimators for a singularly perturbed reaction-diffusion equation. Numer. Math. 78(3), 479\u2013493 (1998)","journal-title":"Numer. Math."},{"issue":"4","key":"9327_CR22","doi-asserted-by":"crossref","first-page":"3180","DOI":"10.1137\/080726239","volume":"47","author":"R Verf\u00fcrth","year":"2009","unstructured":"Verf\u00fcrth, R.: A note on constant-free a posteriori error estimates. SIAM J. Numer. Anal. 47(4), 3180\u20133194 (2009)","journal-title":"SIAM J. Numer. Anal."},{"key":"9327_CR23","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1007\/s10915-010-9410-1","volume":"46","author":"M Vohral\u013ak","year":"2011","unstructured":"Vohral\u013ak, M.: Guaranteed and fully robust a posteriori error estimates for conforming discretizations of diffusion problems with discontinuous coefficients. J. Sci. Comput. 46, 397\u2013438 (2011)","journal-title":"J. Sci. Comput."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-013-9327-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-013-9327-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-013-9327-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T17:08:18Z","timestamp":1559149698000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-013-9327-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,10,26]]},"references-count":23,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2014,8]]}},"alternative-id":["9327"],"URL":"https:\/\/doi.org\/10.1007\/s10444-013-9327-y","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,10,26]]}}}