{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T17:50:21Z","timestamp":1779126621399,"version":"3.51.4"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2002,1,1]],"date-time":"2002-01-01T00:00:00Z","timestamp":1009843200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2002,1,1]],"date-time":"2002-01-01T00:00:00Z","timestamp":1009843200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Computational Mathematics"],"published-print":{"date-parts":[[2002,1]]},"DOI":"10.1023\/a:1014221125034","type":"journal-article","created":{"date-parts":[[2002,12,29]],"date-time":"2002-12-29T19:13:07Z","timestamp":1041189187000},"page":"47-75","source":"Crossref","is-referenced-by-count":95,"title":["A Posteriori Error Estimators for Elliptic Equations with Discontinuous Coefficients"],"prefix":"10.1007","volume":"16","author":[{"given":"Martin","family":"Petzoldt","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"387380_CR1","volume-title":"Pure and Applied Mathematics, Vol. 65","author":"R.A. Adams","year":"1975","unstructured":"R.A. Adams, Sobolev Spaces, Pure and Applied Mathematics, Vol. 65 (Academic Press, New York\/London, 1975)."},{"issue":"2","key":"387380_CR2","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1137\/S003614299732187X","volume":"36","author":"M. Ainsworth","year":"1998","unstructured":"M. Ainsworth and I. Babuska, Reliable and robust a posteriori error estimation for singularly perturbed reaction-diffusion problems, SIAM J. Numer. Anal. 36(2) (1998) 331-353.","journal-title":"SIAM J. Numer. Anal."},{"key":"387380_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":"M. Ainsworth and T. Oden, A Posteriori Error Estimation in Finite Element Analysis (Wiley, New York, 2000)."},{"key":"387380_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-22101-3","volume-title":"Lineare Funktionalanalysis","author":"H.W. Alt","year":"1992","unstructured":"H.W. Alt, Lineare Funktionalanalysis (Springer, Berlin, 1992)."},{"key":"387380_CR5","volume-title":"Anisotropic Finite Elements: Local Estimates and Applications","author":"T. Apel","year":"1999","unstructured":"T. Apel, Anisotropic Finite Elements: Local Estimates and Applications (Teubner, Stuttgart, 1999)."},{"issue":"24","key":"387380_CR6","doi-asserted-by":"crossref","first-page":"4207","DOI":"10.1002\/nme.1620382408","volume":"38","author":"I. Babuska","year":"1995","unstructured":"I. Babuska, T. Strouboulis, C.S. Upadhyay and S.K. Gangaraj, A posteriori estimation and adaptive control of the pollution error in the h-version of the finite element method, Internat. J. Numer.Methods Engrg. 38(24) (1995) 4207-4235.","journal-title":"Internat. J. Numer.Methods Engrg."},{"issue":"4","key":"387380_CR7","doi-asserted-by":"crossref","first-page":"921","DOI":"10.1137\/0730048","volume":"30","author":"R.E. Bank","year":"1993","unstructured":"R.E. Bank and R.K. Smith, A posteriori error estimates based on hierachical bases, SIAM J. Numer. Anal. 30(4) (1993) 921-935.","journal-title":"SIAM J. Numer. Anal."},{"key":"387380_CR8","series-title":"Technical Report","volume-title":"KASKADE 3.0-an object oriented finite element code","author":"R. Beck","year":"1994","unstructured":"R. Beck, B. Erdmann and R. Roitzsch, KASKADE 3.0-an object oriented finite element code, Technical Report 95-4, Konrad-Zuse-Zentrum f\u00fcr Informationstechnik, Berlin (1994)."},{"issue":"4","key":"387380_CR9","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1007\/PL00005393","volume":"85","author":"C. Bernardi","year":"2000","unstructured":"C. Bernardi and R. Verf\u00fcrth, Adaptive finite element methods for elliptic equations with non-smooth coefficients, Numer. Math. 85(4) (2000) 579-608.","journal-title":"Numer. Math."},{"key":"387380_CR10","doi-asserted-by":"crossref","first-page":"1188","DOI":"10.1137\/0733059","volume":"33","author":"F. Bornemann","year":"1996","unstructured":"F. Bornemann, B. Erdmann and R. Kornhuber, A posteriori error estimates for elliptic problems in two and three space dimensions, SIAM J. Numer. Anal. 33 (1996) 1188-1204.","journal-title":"SIAM J. Numer. Anal."},{"key":"387380_CR11","first-page":"463","volume":"56","author":"J.H. Bramble","year":"1991","unstructured":"J.H. Bramble and Jinchao Xu, Some estimates for a weighted L\n2-projection, Math. Comp. 56 (1991) 463-476.","journal-title":"Math. Comp."},{"key":"387380_CR12","first-page":"17","volume-title":"Handbook of Numerical Analysis, Vol. II","author":"P.G. Ciarlet","year":"1991","unstructured":"P.G. Ciarlet, Basic error estimates for elliptic problems, in: Handbook of Numerical Analysis, Vol. II (North-Holland, Amsterdam, 1991) pp. 17-352."},{"issue":"3","key":"387380_CR13","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1051\/m2an:1999155","volume":"33","author":"M. Costabel","year":"1999","unstructured":"M. Costabel, M. Dauge and S. Nicaise, Singularities of Maxwell interface problems, Math. Model. Numer. Anal. 33(3) (1999) 627-649.","journal-title":"Math. Model. Numer. Anal."},{"key":"387380_CR14","unstructured":"M. Dobrowolski, Numerical approximation of elliptic interface problems and corner problems, Habilitationsschrift, Math. Fak. Univ. Bonn (1981)."},{"issue":"3","key":"387380_CR15","doi-asserted-by":"crossref","first-page":"1106","DOI":"10.1137\/0733054","volume":"33","author":"W. D\u00f6rfler","year":"1996","unstructured":"W. D\u00f6rfler, A convergent adaptive algorithm for Poisson's equation, SIAM J. Numer. Anal. 33(3) (1996) 1106-1124.","journal-title":"SIAM J. Numer. Anal."},{"key":"387380_CR16","unstructured":"W. D\u00f6rfler and R.H. Nochetto, Small data oscillation implies the saturation assumption, MSRI preprint 2000-027, MSRI (2000)."},{"issue":"7","key":"387380_CR17","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1002\/1521-4001(200007)80:7<481::AID-ZAMM481>3.0.CO;2-5","volume":"80","author":"W. D\u00f6rfler","year":"2000","unstructured":"W. D\u00f6rfler and O. Wilderotter, An adaptive finite element method for a linear elliptic equation with variable coefficients, Z. Angew. Math. Mech. 80(7) (2000) 481-491.","journal-title":"Z. Angew. Math. Mech."},{"key":"387380_CR18","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1007\/s002110050172","volume":"72","author":"M. Dryja","year":"1996","unstructured":"M. Dryja, M.V. Sarkis and O.B. Widlund, Multilevel Schwarz methods for elliptic problems with discontinuous coefficients in three dimensions, Numer. Math. 72 (1996) 313-348.","journal-title":"Numer. Math."},{"issue":"150","key":"387380_CR19","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1090\/S0025-5718-1980-0559195-7","volume":"34","author":"T. Dupont","year":"1980","unstructured":"T. Dupont and R. Scott, Polynomial approximation of functions in Sobolev spaces, Math. Comp. 34(150) (1980) 441-463.","journal-title":"Math. Comp."},{"key":"387380_CR20","series-title":"Kiel, Notes on Numerical Fluid Mechanics","volume-title":"Proc. of the 14th GAMM Seminar on Concepts of Numerical Software","author":"J. Fuhrmann","year":"1998","unstructured":"J. Fuhrmann, T. Koprucki and H. Langmach, pdelib: An open modular tool box for the numerical solution of partial differential equations. Design patterns, in: Proc. of the 14th GAMM Seminar on Concepts of Numerical Software, Kiel, Notes on Numerical Fluid Mechanics (Vieweg, Braunschweig, 1998)."},{"key":"387380_CR21","volume-title":"Grundlehren der Mathematischen Wissenschaften, Vol. 224","author":"D. Gilbarg","year":"1977","unstructured":"D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Grundlehren der Mathematischen Wissenschaften, Vol. 224 (Springer, Berlin, 1977)."},{"key":"387380_CR22","volume-title":"Elliptic Problems in Nonsmooth Domains","author":"P. Grisvard","year":"1985","unstructured":"P. Grisvard, Elliptic Problems in Nonsmooth Domains (Pitman (Advanced Publishing Program), Boston, MA, 1985)."},{"key":"387380_CR23","series-title":"Research Notes in Applied Mathematics","volume-title":"Singularities in Boundary Value Problems","author":"P. Grisvard","year":"1992","unstructured":"P. Grisvard, Singularities in Boundary Value Problems, Research Notes in Applied Mathematics, Vol. 22 (Springer, Berlin, 1992)."},{"key":"387380_CR24","unstructured":"M. Jung, On adaptive grids in multilevel methods, Technical Report No. 5, Weierstra\u00df-Institut f\u00fcr Angewandte Analysis und Stochastik (1993). M. Petzoldt \/ A posteriori error estimators 75"},{"key":"387380_CR25","first-page":"589","volume-title":"Proc. of a Symposium, University of Maryland, Baltimore, MD, 26-30 June 1972","author":"R.B. Kellogg","year":"1972","unstructured":"R.B. Kellogg, Higher order singularities for interface problems, in: Proc. of a Symposium, University of Maryland, Baltimore, MD, 26-30 June 1972 (Academic Press, New York\/London, 1972) pp. 589-602."},{"key":"387380_CR26","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1080\/00036817408839086","volume":"4","author":"R.B. Kellogg","year":"1975","unstructured":"R.B. Kellogg, On the Poisson equation with intersecting interfaces, Appl. Anal. 4 (1975) 101-129.","journal-title":"Appl. Anal."},{"key":"387380_CR27","unstructured":"T. K\u00fchn, Die Regularit\u00f6t der L\u00f6sungen von Interfaceproblemen in Gebieten mit singul\u00e4ren Punkten, Diplomtheses, Universit\u00e4t Rostock (1992)."},{"key":"387380_CR28","volume-title":"A Posteriori Error Estimation for Anisotropic Tetrahedral and Triangular Finite Element Meshes","author":"G. Kunert","year":"1999","unstructured":"G. Kunert, A Posteriori Error Estimation for Anisotropic Tetrahedral and Triangular Finite Element Meshes (Logos, Berlin, 1999)."},{"key":"387380_CR29","unstructured":"P. Morin, R.H. Nochetto and K.G. Siebert, Local problems on stars: A posteriori error estimators, convergence, and performance, Preprint 29\/00, University of Freiburg (2000)."},{"key":"387380_CR30","volume-title":"Polygonal Interface Problems","author":"S. Nicaise","year":"1993","unstructured":"S. Nicaise, Polygonal Interface Problems (Verlag Peter D. Lang, Frankfurt am Main, 1993)."},{"key":"387380_CR31","volume-title":"Variacionno-Rassnostnye Metody Reshenya Elliptitchyeskikh Uravnenij","author":"L.A. Oganesjan","year":"1979","unstructured":"L.A. Oganesjan and L.A Ruchowiec, Variacionno-Rassnostnye Metody Reshenya Elliptitchyeskikh Uravnenij (Akademia Nauk Armjanskoj SSR, Erevan, 1979)."},{"issue":"2","key":"387380_CR32","doi-asserted-by":"crossref","first-page":"431","DOI":"10.4171\/zaa\/1024","volume":"20","author":"M. Petzoldt","year":"2001","unstructured":"M. Petzoldt, Regularity results for Laplace interface problems in two dimensions, Z. Anal. Anwendungen 20(2) (2001) 431-455.","journal-title":"Z. Anal. Anwendungen"},{"key":"387380_CR33","unstructured":"M. Petzoldt, Regularity and error estimators for elliptic problems with discontinuous coefficients, Ph.D. thesis, FU Berlin, http:\/\/www.diss.fu-berlin.de\/diss (2001) submitted."},{"key":"387380_CR34","volume-title":"An Analysis of the Finite Element Method, Prentice-Hall Series in Automatic Computation","author":"G. Strang","year":"1973","unstructured":"G. Strang and G.J. Fix, An Analysis of the Finite Element Method, Prentice-Hall Series in Automatic Computation (Prentice-Hall, Englewood Cliffs, NJ, 1973)."},{"key":"387380_CR35","unstructured":"R. Verf\u00fcrth, A Review of a Posteriori Error Estimation and Adaptive Mesh Refinement Techniques (Wiley\/Teubner, 1996)."},{"key":"387380_CR36","doi-asserted-by":"crossref","unstructured":"R. Verf\u00fcrth, Robust a posteriori error estimators for a singulary perturbed reaction-diffusion equation, Numer. Math. (1998) 479-493.","DOI":"10.1007\/s002110050322"},{"key":"387380_CR37","first-page":"353","volume-title":"Handbook of Numerical Analysis, Vol. II","author":"L.B. Wahlbin","year":"1991","unstructured":"L.B. Wahlbin, Local behavior in finite element methods, in: Handbook of Numerical Analysis, Vol. II (North-Holland, Amsterdam, 1991) pp. 353-522."},{"key":"387380_CR38","first-page":"563","volume":"57","author":"J. Xu","year":"1991","unstructured":"J. Xu, Counterexamples concerning a weighted L\n2 projection, Math. Comp. 57 (1991) 563-568.","journal-title":"Math. Comp."},{"issue":"2","key":"387380_CR39","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1002\/nme.1620240206","volume":"24","author":"O.C. Zienkiewicz","year":"1987","unstructured":"O.C. Zienkiewicz and J.Z. Zhu, A simple error estimator and adaptive procedure for practical engineering analysis, Internat. J. Numer. Methods Engrg. 24(2) (1987) 337-357.","journal-title":"Internat. J. Numer. Methods Engrg."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1014221125034.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1014221125034\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1014221125034.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,16]],"date-time":"2025-05-16T23:23:49Z","timestamp":1747437829000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1014221125034"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,1]]},"references-count":39,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2002,1]]}},"alternative-id":["387380"],"URL":"https:\/\/doi.org\/10.1023\/a:1014221125034","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,1]]}}}