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The ELLAM-MFEM time-stepping procedure, in which an Eulerian\u2013Lagrangian localized adjoint method (ELLAM) is used to solve the transport equation and a mixed finite element method (MFEM) is used for the pressure equation, simulates porous medium flow accurately even if large spatial grids and time steps are used. In this paper we prove an optimal-order error estimate for a family of ELLAM-MFEM approximations.<\/jats:p>","DOI":"10.1137\/s0036142903428281","type":"journal-article","created":{"date-parts":[[2008,5,4]],"date-time":"2008-05-04T04:04:04Z","timestamp":1209873844000},"page":"2133-2152","source":"Crossref","is-referenced-by-count":45,"title":["An Optimal-Order Error Estimate for a Family of ELLAM-MFEM Approximations to Porous Medium Flow"],"prefix":"10.1137","volume":"46","author":[{"given":"Hong","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,5,2]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/0732017"},{"key":"R2","unstructured":"J. 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Ciarlet,\n                      The Finite Element Method for Elliptic Problems\n                      , North-Holland, Amsterdam, 1978.","DOI":"10.1115\/1.3424474"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1983170100171"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1983170302491"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/0719063"},{"key":"R11","doi-asserted-by":"crossref","unstructured":"R.E. Ewing, ed.\n                      The Mathematics of Reservoir Simulation\n                      , SIAM, Philadelphia, 1984.","DOI":"10.1137\/1.9781611971071"},{"key":"R12","doi-asserted-by":"crossref","unstructured":"R.E. Ewing, T.F. Russell, and M.F. Wheeler,\n                      Simulation of miscible displacement using mixed methods and a modified method of characteristics\n                      , SPE 12241, (1983), pp. 71\u201381.","DOI":"10.2523\/12241-MS"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(84)90048-3"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370489"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/0733017"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(00)00522-7"},{"key":"R17","unstructured":"C.I. Heberton, T.F. Russell, L.F. Konikow, and G.Z. Hornberger,\n                      Three-dimensional finite-volume ELLAM implementation\n                      , in Computational Methods in Water Resources XIII, L. Bently et al. eds., Balkema, Rotterdam, pp. 603\u2013610."},{"key":"R18","unstructured":"K.W. 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Ewing, ed., SIAM, Philadelphia, 1984, pp. 35\u2013106.","DOI":"10.1137\/1.9781611971071.ch2"},{"key":"R23","unstructured":"V. Thom\u00e9e,\n                      Galerkin Finite Element Methods for Parabolic Problems\n                      , Lecture Notes in Math. 1054, Springer-Verlag, New York, 1984."},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1098-2426(199811)14:6<739::AID-NUM3>3.0.CO;2-R"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142998335686"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827596309396"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1002\/num.1690110103"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1999.6239"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/15.3.405"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827598349215"},{"key":"R31","first-page":"286","volume":"5","author":"Wang K.","year":"2008","journal-title":"Internat. J. 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