{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,21]],"date-time":"2023-11-21T11:59:19Z","timestamp":1700567959872},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2017,9,27]],"date-time":"2017-09-27T00:00:00Z","timestamp":1506470400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung (CH)","award":["200021-162990"],"award-info":[{"award-number":["200021-162990"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2018,4]]},"DOI":"10.1007\/s10915-017-0565-x","type":"journal-article","created":{"date-parts":[[2017,9,27]],"date-time":"2017-09-27T07:31:57Z","timestamp":1506497517000},"page":"111-127","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["hp-Adaptive Galerkin Time Stepping Methods for Nonlinear Initial Value Problems"],"prefix":"10.1007","volume":"75","author":[{"given":"Irene","family":"Kyza","sequence":"first","affiliation":[]},{"given":"Stephen","family":"Metcalfe","sequence":"additional","affiliation":[]},{"given":"Thomas P.","family":"Wihler","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,9,27]]},"reference":[{"issue":"254","key":"565_CR1","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1090\/S0025-5718-05-01800-4","volume":"75","author":"G Akrivis","year":"2006","unstructured":"Akrivis, G., Makridakis, C., Nochetto, R.H.: A posteriori error estimates for the Crank-Nicolson method for parabolic equations. Math. Comput. 75(254), 511\u2013531 (2006)","journal-title":"Math. Comput."},{"issue":"1","key":"565_CR2","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1007\/s00211-009-0254-2","volume":"114","author":"G Akrivis","year":"2009","unstructured":"Akrivis, G., Makridakis, C., Nochetto, R.H.: Optimal order a posteriori error estimates for a class of Runge-Kutta and Galerkin methods. Numer. Math. 114(1), 133\u2013160 (2009)","journal-title":"Numer. Math."},{"key":"565_CR3","series-title":"Lectures in Mathematics, ETH Z\u00fcrich","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-7605-6","volume-title":"Adaptive Finite Element Methods for Differential Equations","author":"W Bangerth","year":"2003","unstructured":"Bangerth, W., Rannacher, R.: Adaptive Finite Element Methods for Differential Equations. Lectures in Mathematics, ETH Z\u00fcrich. Birkh\u00e4user Verlag, Basel (2003)"},{"key":"565_CR4","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1137\/040619314","volume":"44","author":"H Brunner","year":"2006","unstructured":"Brunner, H., Sch\u00f6tzau, D.: $$hp$$ h p -discontinuous Galerkin time-stepping for Volterra integrodifferential equations. SIAM J. Numer. Anal. 44, 224\u2013245 (2006)","journal-title":"SIAM J. Numer. Anal."},{"key":"565_CR5","doi-asserted-by":"crossref","unstructured":"Cangiani, A., Georgoulis, E.H., Kyza, I., Metcalfe, S.: Adaptivity and blow-up detection for nonlinear evolution problems. SIAM J. Sci. Comput. 38, A3833\u2013A3856 (2016)","DOI":"10.1137\/16M106073X"},{"key":"565_CR6","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/s00211-008-0165-7","volume":"110","author":"E Cuesta","year":"2008","unstructured":"Cuesta, E., Makridakis, C.: A posteriori error estimates and maximal regularity for approximations of fully nonlinear parabolic problems in Banach spaces. Numer. Math. 110, 257\u2013275 (2008)","journal-title":"Numer. Math."},{"key":"565_CR7","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1090\/S0025-5718-1981-0606506-0","volume":"36","author":"M Delfour","year":"1981","unstructured":"Delfour, M., Hager, W., Trochu, F.: Discontinuous Galerkin methods for ordinary differential equations. Math. Comput. 36, 455\u2013473 (1981)","journal-title":"Math. Comput."},{"issue":"175","key":"565_CR8","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1090\/S0025-5718-1986-0842129-0","volume":"47","author":"MC Delfour","year":"1986","unstructured":"Delfour, M.C., Dubeau, F.: Discontinuous polynomial approximations in the theory of one-step, hybrid and multistep methods for nonlinear ordinary differential equations. Math. Comput. 47(175), 169\u2013189, S1\u2013S8 (1986)","journal-title":"Math. Comput."},{"key":"565_CR9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/0732001","volume":"32","author":"D Estep","year":"1995","unstructured":"Estep, D.: A posteriori error bounds, global error control for approximation of ordinary differential equations. SIAM J. Numer. Anal. 32, 1\u201348 (1995)","journal-title":"SIAM J. Numer. Anal."},{"key":"565_CR10","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1051\/m2an\/1994280708151","volume":"28","author":"D Estep","year":"1994","unstructured":"Estep, D., French, D.: Global error control for the continuous Galerkin finite element method for ordinary differential equations. RAIRO Mod\u00e9l. Math. Anal. Num\u00e9r. 28, 815\u2013852 (1994)","journal-title":"RAIRO Mod\u00e9l. Math. Anal. Num\u00e9r."},{"issue":"4","key":"565_CR11","doi-asserted-by":"crossref","first-page":"854","DOI":"10.1016\/j.camwa.2013.05.024","volume":"67","author":"T Fankhauser","year":"2014","unstructured":"Fankhauser, T., Wihler, T.P., Wirz, M.: The hp-adaptive FEM based on continuous Sobolev embeddings: isotropic refinements. Comput. Math. Appl. 67(4), 854\u2013868 (2014)","journal-title":"Comput. Math. Appl."},{"key":"565_CR12","doi-asserted-by":"crossref","unstructured":"Janssen, B., Wihler, T.P.: Existence results for the continuous and discontinuous Galerkin time stepping methods for nonlinear initial value problems, arXiv preprint. arXiv:1407.5520 (2014)","DOI":"10.1007\/978-3-319-19800-2_7"},{"key":"565_CR13","doi-asserted-by":"crossref","first-page":"908","DOI":"10.1137\/0725051","volume":"25","author":"C Johnson","year":"1988","unstructured":"Johnson, C.: Error estimates and adaptive time-step control for a class of one-step methods for stiff ordinary differential equations. SIAM J. Numer. Anal. 25, 908\u2013926 (1988)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"565_CR14","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1051\/m2an:2004006","volume":"38","author":"D Kessler","year":"2004","unstructured":"Kessler, D., Nochetto, R.H., Schmidt, A.: A posteriori error control for the Allen-Cahn problem: circumventing Gronwall\u2019s inequality. ESAIM Math. Model. Numer. Anal. 38(1), 129\u2013142 (2004). (Eng)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"issue":"1","key":"565_CR15","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1137\/100796819","volume":"49","author":"I Kyza","year":"2011","unstructured":"Kyza, I., Makridakis, C.: Analysis for time discrete approximations of blow-up solutions of semilinear parabolic equations. SIAM J. Numer. Anal. 49(1), 405\u2013426 (2011)","journal-title":"SIAM J. Numer. Anal."},{"issue":"4","key":"565_CR16","doi-asserted-by":"crossref","first-page":"2757","DOI":"10.1137\/080715135","volume":"31","author":"A Lozinski","year":"2009","unstructured":"Lozinski, A., Picasso, M., Prachittham, V.: An anisotropic error estimator for the Crank-Nicolson method: application to a parabolic problem. SIAM J. Sci. Comput. 31(4), 2757\u20132783 (2009)","journal-title":"SIAM J. Sci. Comput."},{"issue":"4","key":"565_CR17","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1007\/s00211-006-0013-6","volume":"104","author":"C Makridakis","year":"2006","unstructured":"Makridakis, C., Nochetto, R.H.: A posteriori error analysis for higher order dissipative methods for evolution problems. Numer. Math. 104(4), 489\u2013514 (2006)","journal-title":"Numer. Math."},{"issue":"1","key":"565_CR18","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1145\/2629459","volume":"41","author":"WF Mitchell","year":"2014","unstructured":"Mitchell, W.F., McClain, M.A.: A comparison of hp-adaptive strategies for elliptic partial differential equations. ACM Trans. Math. Softw. (TOMS) 41(1), 2 (2014)","journal-title":"ACM Trans. Math. Softw. (TOMS)"},{"key":"565_CR19","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s100920070002","volume":"37","author":"D Sch\u00f6tzau","year":"2000","unstructured":"Sch\u00f6tzau, D., Schwab, C.: An $$hp$$ h p a-priori error analysis of the DG time-stepping method for initial value problems. Calcolo 37, 207\u2013232 (2000)","journal-title":"Calcolo"},{"key":"565_CR20","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1137\/S0036142999352394","volume":"38","author":"D Sch\u00f6tzau","year":"2000","unstructured":"Sch\u00f6tzau, D., Schwab, C.: Time discretization of parabolic problems by the $$hp$$ h p -version of the discontinuous Galerkin finite element method. SIAM J. Numer. Anal. 38, 837\u2013875 (2000)","journal-title":"SIAM J. Numer. Anal."},{"key":"565_CR21","doi-asserted-by":"crossref","first-page":"1121","DOI":"10.1016\/S0764-4442(01)02186-3","volume":"333","author":"D Sch\u00f6tzau","year":"2001","unstructured":"Sch\u00f6tzau, D., Schwab, C.: $$hp$$ h p -discontinuous Galerkin time-stepping for parabolic problems. C. R. Acad. Sci. Paris, S\u00e9rie I 333, 1121\u20131126 (2001)","journal-title":"C. R. Acad. Sci. Paris, S\u00e9rie I"},{"issue":"3","key":"565_CR22","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1007\/s00211-009-0285-8","volume":"115","author":"D Sch\u00f6tzau","year":"2010","unstructured":"Sch\u00f6tzau, D., Wihler, T.P.: A posteriori error estimation for $$hp$$ h p -version time-stepping methods for parabolic partial differential equations. Numer. Math. 115(3), 475\u2013509 (2010)","journal-title":"Numer. Math."},{"key":"565_CR23","doi-asserted-by":"crossref","first-page":"6685","DOI":"10.1016\/S0045-7825(01)00258-4","volume":"190","author":"T Werder","year":"2001","unstructured":"Werder, T., Gerdes, K., Sch\u00f6tzau, D., Schwab, C.: $$hp$$ h p -discontinuous Galerkin time-stepping for parabolic problems. Comput. Methods Appl. Mech. Engrg. 190, 6685\u20136708 (2001)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"565_CR24","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1007\/s10915-004-4796-2","volume":"25","author":"TP Wihler","year":"2005","unstructured":"Wihler, T.P.: An a-priori error analysis of the $$hp$$ h p -version of the continuous Galerkin FEM for nonlinear initial value problems. J. Sci. Comput. 25, 523\u2013549 (2005)","journal-title":"J. Sci. Comput."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-017-0565-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0565-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0565-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,3]],"date-time":"2022-08-03T14:18:15Z","timestamp":1659536295000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-017-0565-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,27]]},"references-count":24,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,4]]}},"alternative-id":["565"],"URL":"https:\/\/doi.org\/10.1007\/s10915-017-0565-x","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,27]]}}}