{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T01:19:03Z","timestamp":1648948743777},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2007,11,21]],"date-time":"2007-11-21T00:00:00Z","timestamp":1195603200000},"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":[[2008,11]]},"DOI":"10.1007\/s10444-007-9052-5","type":"journal-article","created":{"date-parts":[[2007,11,20]],"date-time":"2007-11-20T04:47:20Z","timestamp":1195534040000},"page":"337-356","source":"Crossref","is-referenced-by-count":2,"title":["Asymptotic expansions and Richardson extrapolation of approximate solutions for integro-differential equations by mixed finite element methods"],"prefix":"10.1007","volume":"29","author":[{"given":"Shanghui","family":"Jia","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Deli","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuhua","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2007,11,21]]},"reference":[{"key":"9052_CR1","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/BF01389427","volume":"49","author":"H. Blum","year":"1986","unstructured":"Blum, H., Lin, Q., Rannacher, R.: Asymptotic error expansion and Richardson extrapolation for linear finite elements. Numer. Math. 49, 11\u201338 (1986)","journal-title":"Numer. Math."},{"key":"9052_CR2","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1216\/jiea\/1181074245","volume":"10","author":"H. Brunner","year":"1998","unstructured":"Brunner, H., Lin, Y., Zhang, S.: Higher accuracy methods for second-kind Volterra integral equations based on asymptotic expansions of iterated Galerkin methods. J. Integral Equations Appl. 10, 375\u2013396 (1998)","journal-title":"J. Integral Equations Appl."},{"issue":"3","key":"9052_CR3","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/BF02575943","volume":"25","author":"J.R. Cannon","year":"1988","unstructured":"Cannon, J.R., Lin, Y.: Non-classical H 1 projection and Galerkin methods for nonlinear parabolic integro-differential equations. Calcolo 25(3), 187\u2013201 (1988)","journal-title":"Calcolo"},{"issue":"3","key":"9052_CR4","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1137\/0727036","volume":"27","author":"J.R. Cannon","year":"1990","unstructured":"Cannon, J.R., Lin, Y.: A priori L 2 error estimates for finite element methods for nonlinear diffusion equations with memory. SIAM J. Numer. Anal. 27(3), 595\u2013607 (1990)","journal-title":"SIAM J. Numer. Anal."},{"key":"9052_CR5","volume-title":"Higher Accuracy Theory of FEM","author":"C. Chen","year":"1995","unstructured":"Chen, C., Huang, Y.: Higher Accuracy Theory of FEM. Hunan Science Press, Changsha (1995)"},{"key":"9052_CR6","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1090\/S0025-5718-1985-0771029-9","volume":"44","author":"J. Douglas Jr.","year":"1985","unstructured":"Douglas, J., Jr., Roberts, J.E.: Global estimates for mixed methods for second order elliptic equations. Math. Comp. 44, 39\u201352 (1985)","journal-title":"Math. Comp."},{"key":"9052_CR7","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/978-1-4612-2012-1_16","volume-title":"Current and Future Directions in Applied Mathematics","author":"R.E. Ewing","year":"1997","unstructured":"Ewing, R.E.: Mathematical modeling and simulation for applications of fluid flow in porous media. In: M. Alber, Hu, B., Rosenthal, J. (eds.) Current and Future Directions in Applied Mathematics, pp. 161\u2013182. Birkhauser, Berlin, Germany (1997)"},{"key":"9052_CR8","first-page":"227","volume-title":"Proceedings of Next Generation Environmental Models and Computational Methods","author":"R.E. Ewing","year":"1997","unstructured":"Ewing, R.E.: The need for multidisciplinary involvement in groundwater contaminant simulations. In: Delic, G., Wheeler, M. (eds.) Proceedings of Next Generation Environmental Models and Computational Methods, pp. 227\u2013245. SIAM, Philadelphia, PA (1997)"},{"key":"9052_CR9","doi-asserted-by":"crossref","first-page":"1538","DOI":"10.1137\/S0036142900378406","volume":"40","author":"R.E. Ewing","year":"2002","unstructured":"Ewing, R.E., Lin, Y., Sun, T., Wang, J., Zhang, S.: Sharp L 2 error estimates and superconvergence of mixed finite element methods for nonFickian flows in porous media. SIAM J. Numer. Anal. 40, 1538\u20131560 (2002)","journal-title":"SIAM J. Numer. Anal."},{"key":"9052_CR10","first-page":"301","volume":"2","author":"R.E. Ewing","year":"2005","unstructured":"Ewing, R.E., Lin, Y., Wang, J., Zhang, S.: L \u2009\u221e\u2009-error estimates and superconvergence in maximum norm of mixed finite element methods for nonFickian flows in porous media. Int. J. Numer. Anal. Model. 2, 301\u2013328 (2005)","journal-title":"Int. J. Numer. Anal. Model."},{"key":"9052_CR11","first-page":"75","volume":"70","author":"R.E. Ewing","year":"2001","unstructured":"Ewing, R.E., Lin, Y., Wang, J.: A numerical approximation of nonFickian flows with mixing length growth in porous media. Acta Math. Univ. Comentian. (N. S.). 70, 75\u201384 (2001)","journal-title":"Acta Math. Univ. Comentian. (N. S.)."},{"key":"9052_CR12","first-page":"283","volume":"13","author":"R.E. Ewing","year":"2006","unstructured":"Ewing, R.E., Lin, Y., Wang, J., Yang, X.: Backward Euler mixed FEM and regularity of parabolic integro-differential equations with non-smooth data. Dyn. Contin. Discrete Impuls. Syst. 13, 283\u2013295 (2006)","journal-title":"Dyn. Contin.Discrete Impuls. Syst."},{"key":"9052_CR13","doi-asserted-by":"crossref","first-page":"1122","DOI":"10.1137\/040614293","volume":"44","author":"G. Fairweather","year":"2006","unstructured":"Fairweather, G., Lin, Q., Lin, Y., J. Wang, Zhang, S.: Asymptotic expansions and Richardson extrapolation of approximate solutions for second order elliptic problems by mixed finite element methods. SIAM J. Numer. Anal. 44, 1122\u20131149 (2006)","journal-title":"SIAM J. Numer. Anal."},{"key":"9052_CR14","first-page":"11","volume":"158","author":"P. Helfrich","year":"1983","unstructured":"Helfrich, P.: Asymptotic expansion for the finite element approximations of parabolic problems. Bonner Math. Schriften 158, 11\u201330 (1983)","journal-title":"Bonner Math. Schriften"},{"key":"9052_CR15","doi-asserted-by":"crossref","first-page":"1535","DOI":"10.1137\/0727090","volume":"27","author":"Q. Lin","year":"1990","unstructured":"Lin, Q., Sloan, I.H., Xie, R.: Extrapolation of the iterated-collocation method for integral equations of the second kind. SIAM J. Numer. Anal. 27, 1535\u20131541 (1990)","journal-title":"SIAM J. Numer. Anal."},{"key":"9052_CR16","unstructured":"Lin, Q., Yan, N.: The Construction and Analysis of High Efficiency Finite Element Methods. Hebei University Publishers (1996)"},{"key":"9052_CR17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/A:1022264125558","volume":"42","author":"Q. Lin","year":"1997","unstructured":"Lin, Q., Zhang, S.: An immediate analysis for global superconvergence for integrodifferential equations. Appl. Math. 42, 1\u201321 (1997)","journal-title":"Appl. Math."},{"key":"9052_CR18","first-page":"57","volume":"16","author":"Q. Lin","year":"1998","unstructured":"Lin, Q., Zhang, S., Yan, N.: Asymptotic error expansion and defect correction for Sobolev and viscoelasticity type equations. J. Comput. Math. 16, 57\u201362 (1998)","journal-title":"J. Comput. Math."},{"key":"9052_CR19","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1007\/BF02677428","volume":"14","author":"Q. Lin","year":"1998","unstructured":"Lin, Q., Zhang, S., Yan, N.: High accuracy analysis for integrodifferential equations. Acta Math. Appl. Sinica 14, 202\u2013211 (1998)","journal-title":"Acta Math. Appl. Sinica"},{"key":"9052_CR20","first-page":"282","volume":"10","author":"Q. Lin","year":"1997","unstructured":"Lin, Q., Zhang, S., Yan, N.: Methods for improving approximate accuracy for hyperbolic integro-differential equations. Systems Sci. Math. Sci. 10, 282\u2013288 (1997)","journal-title":"Systems Sci. Math. Sci."},{"key":"9052_CR21","first-page":"409","volume":"17","author":"Q. Lin","year":"1997","unstructured":"Lin, Q., Zhang, S., Yan, N.: Extrapolation and defect correction for diffusion equations with boundary integral conditions. Acta Math. Sci. 17, 409\u2013412 (1997)","journal-title":"Acta Math. Sci."},{"key":"9052_CR22","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1023\/A:1018925103993","volume":"9","author":"Q. Lin","year":"1998","unstructured":"Lin, Q., Zhang, S., Yan, N.: An acceleration method for integral equations by using interpolation post-processing. Adv. Comput. Math. 9, 117\u2013128 (1998)","journal-title":"Adv. Comput. Math."},{"issue":"2","key":"9052_CR23","first-page":"159","volume":"15","author":"Y. Lin","year":"1997","unstructured":"Lin, Y.: On maximum norm estimates for Ritz\u2013Volterra projections and applications to some time-dependent problems. J. Comput. Math. 15(2), 159\u2013178 (1997)","journal-title":"J. Comput. Math."},{"issue":"4","key":"9052_CR24","doi-asserted-by":"crossref","first-page":"1047","DOI":"10.1137\/0728056","volume":"28","author":"Y. Lin","year":"1991","unstructured":"Lin, Y., Thom\u00e9e, V., Wahlbin, L.: Ritz\u2013Volterra projection onto finite element spaces and applications to integrodifferential and related equations. SIAM J. Numer. Anal. 28(4), 1047\u20131070 (1991)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"9052_CR25","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1137\/S0036142999336145","volume":"38","author":"T. Lin","year":"2000","unstructured":"Lin, T., Lin, Y., Rao, M., Zhang, S.: Petrov\u2013Galerkin methods for linear Volterra integro-differential equations. SIAM J. Numer. Anal. 38(3), 937\u2013963 (2000)","journal-title":"SIAM J. Numer. Anal."},{"key":"9052_CR26","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-8224-9","volume-title":"Difference Methods and Their Extrapolation","author":"G. Marchuk","year":"1983","unstructured":"Marchuk, G., Shaidurov, V.: Difference Methods and Their Extrapolation. Springer, New York (1983)"},{"key":"9052_CR27","doi-asserted-by":"crossref","first-page":"1052","DOI":"10.1137\/0723073","volume":"23","author":"I.H. Sloan","year":"1986","unstructured":"Sloan, I.H., Thom\u00e9e, V.: Time discretization of an integro-differential equation of parabolic type. SIAM J. Numer. Anal. 23, 1052\u20131061 (1986)","journal-title":"SIAM J. Numer. Anal."},{"issue":"187","key":"9052_CR28","doi-asserted-by":"crossref","first-page":"121","DOI":"10.2307\/2008352","volume":"53","author":"V. Thom\u00e9e","year":"1989","unstructured":"Thom\u00e9e, V., Zhang, N.: Error estimates for semidiscrete finite element methods for parabolic integro-differential equations. Math. Comp. 53(187), 121\u2013139 (1989)","journal-title":"Math. Comp."},{"key":"9052_CR29","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1090\/S0025-5718-1991-1068807-0","volume":"56","author":"J. Wang","year":"1991","unstructured":"Wang, J.: Superconvergence and extrapolation for mixed finite element methods on rectangular domains. Math. Comp. 56, 477\u2013503 (1991)","journal-title":"Math. Comp."},{"key":"9052_CR30","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/BF01396046","volume":"55","author":"J. Wang","year":"1989","unstructured":"Wang, J.: Asymptotic expansions and L \u2009\u221e\u2009-error estimates for mixed finite element methods for second order elliptic problems. Numer. Math. 55, 401\u2013430 (1989)","journal-title":"Numer. Math."},{"key":"9052_CR31","first-page":"217","volume":"2","author":"N. Yan","year":"1989","unstructured":"N. Yan, Li, K., An extrapolation method for BEM. J. Comput. Math. 2, 217\u2013224 (1989)","journal-title":"J. Comput. Math."},{"key":"9052_CR32","first-page":"407","volume":"19","author":"S. Zhang","year":"2001","unstructured":"Zhang, S., Lin, T., Lin, Y., Rao, M.: Extrapolation and a-posteriori error estimators of Petrov\u2013Galerkin methods for non-linear Volterra integro-differential equations. J. Comput. Math. 19, 407\u2013422 (2001)","journal-title":"J. Comput. Math."},{"key":"9052_CR33","first-page":"253","volume":"10","author":"A. Zhou","year":"1997","unstructured":"Zhou, A., Liem, C.B., Shih, T.M., L\u00fc T.: A multi-parameter splitting extrapolation and a parallel algorithm. Systems Sci. Math. Sci. 10, 253\u2013260 (1997)","journal-title":"Systems Sci. Math. Sci."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-007-9052-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-007-9052-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-007-9052-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T13:08:10Z","timestamp":1559135290000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-007-9052-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,11,21]]},"references-count":33,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,11]]}},"alternative-id":["9052"],"URL":"https:\/\/doi.org\/10.1007\/s10444-007-9052-5","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,11,21]]}}}