{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:21:35Z","timestamp":1787329295716,"version":"build-2736575974"},"reference-count":15,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>In this paper we analyze the convergence properties of full discretizations of a class of generalized porous medium equations. For the spatial and time discretizations, we use continuous piecewise linear finite elements and algebraically stable Runge\u2013Kutta methods, respectively. We prove our convergence result without any assumption on the spatial regularity. It is shown that, under a certain stability assumption, the temporal order of convergence is given by the stage order of the method, whereas the spatial order is essentially one. Numerical experiments illustrate our stability assumption and the convergence result.<\/jats:p>","DOI":"10.1137\/070680953","type":"journal-article","created":{"date-parts":[[2008,4,11]],"date-time":"2008-04-11T18:08:26Z","timestamp":1207937306000},"page":"1769-1779","source":"Crossref","is-referenced-by-count":1,"title":["Finite Element Runge\u2013Kutta Discretizations of Porous Medium\u2013Type Equations"],"prefix":"10.1137","volume":"46","author":[{"given":"Eskil","family":"Hansen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexander","family":"Ostermann","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,4,11]]},"reference":[{"key":"R1","unstructured":"R. A. Adams,\n                      Sobolev Spaces\n                      , Academic Press, New York, London, 1975."},{"key":"R2","unstructured":"V. Barbu,\n                      Analysis and Control of Nonlinear Infinite-Dimensional Systems\n                      , Academic Press, Boston, MA, 1993."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142993258191"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"S. C. Brenner and L. R. Scott,\n                      The Mathematical Theory of Finite Element Methods\n                      , Springer-Verlag, New York, 1994.","DOI":"10.1007\/978-1-4757-4338-8"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"H. Br\u00e9zis,\n                      Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations\n                      , in Contributions to Nonlinear Functional Analysis (Proceedings of the Symposium, Math. Res. 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Wanner,\n                      Solving Ordinary Differential Equations\n                      II.\n                      Stiff and Differential-Algebraic Problems\n                      , 2nd ed., Springer-Verlag, Berlin, 1996.","DOI":"10.1007\/978-3-642-05221-7_1"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-05-01866-1"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/0725046"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1007\/s002110100330"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1137\/0733004"},{"key":"R14","unstructured":"J. L. V\u00e1zquez,\n                      The Porous Medium Equation. Mathematical Theory\n                      , Oxford University Press, Oxford, 2007."},{"key":"R15","doi-asserted-by":"crossref","unstructured":"E. Zeidler,\n                      Nonlinear Functional Analysis and Its Applications\n                      II\/B.\n                      Nonlinear Monotone Operators\n                      , Springer-Verlag, New York, 1990.","DOI":"10.1007\/978-1-4612-0981-2"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/070680953","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:13:58Z","timestamp":1787325238000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/070680953"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":15,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/070680953"],"URL":"https:\/\/doi.org\/10.1137\/070680953","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}