{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T14:30:54Z","timestamp":1773498654440,"version":"3.50.1"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,3,5]],"date-time":"2016-03-05T00:00:00Z","timestamp":1457136000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"crossref","award":["91430104"],"award-info":[{"award-number":["91430104"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"crossref","award":["11271145"],"award-info":[{"award-number":["11271145"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100013286","name":"Specialized Research Fund for the Doctoral Program of Higher Education","doi-asserted-by":"crossref","award":["20114407110009"],"award-info":[{"award-number":["20114407110009"]}],"id":[{"id":"10.13039\/501100013286","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2016,10]]},"DOI":"10.1007\/s10915-016-0187-8","type":"journal-article","created":{"date-parts":[[2016,3,5]],"date-time":"2016-03-05T09:59:06Z","timestamp":1457171946000},"page":"28-51","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["$$L^p$$ L p Error Estimates of Two-Grid Method for Miscible Displacement Problem"],"prefix":"10.1007","volume":"69","author":[{"given":"Yanping","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiaoyan","family":"Zeng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,3,5]]},"reference":[{"key":"187_CR1","volume-title":"Fundamentals of Numerical Reservoir Simulation","author":"DW Peaceman","year":"2000","unstructured":"Peaceman, D.W.: Fundamentals of Numerical Reservoir Simulation. Elsevier, Philadelphia (2000)"},{"key":"187_CR2","doi-asserted-by":"crossref","unstructured":"Russell, T.F.L.: Finite elements with characteristics for two-component incompressible miscible displacement. In: Proceedings of the 6th SPE Symposium on Reservoir Simulation, pp. 123\u2013135. New Orleans (1982)","DOI":"10.2118\/10500-MS"},{"issue":"1","key":"187_CR3","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1051\/m2an\/1983170100171","volume":"17","author":"J Douglas Jr","year":"1983","unstructured":"Douglas Jr., J., Ewing, R.E., Wheeler, M.F.: The approximation of the pressure by a mixed method in the simulation of miscible displacement. RAIRO Anal. Numer. 17(1), 17\u201333 (1983)","journal-title":"RAIRO Anal. Numer."},{"issue":"2","key":"187_CR4","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1137\/S0036141097319152","volume":"30","author":"ZX Chen","year":"1999","unstructured":"Chen, Z.X., Ewing, R.: Mathematical analysis for reservoir models. SIAM J. Math. Anal. 30(2), 431\u2013453 (1999)","journal-title":"SIAM J. Math. Anal."},{"key":"187_CR5","volume-title":"Principles of Applied Reservoir Simulation","author":"JR Fanchi","year":"2005","unstructured":"Fanchi, J.R.: Principles of Applied Reservoir Simulation. Gulf Professional Publishing, Houston (2005)"},{"key":"187_CR6","doi-asserted-by":"crossref","unstructured":"Chen, Z.X.: Reservoir simulation: mathematical techniques in oil recovery. CBMS-NSF Reg. Conf. Ser. Appl. Math. 77, SIAM, Philadelphia (2007)","DOI":"10.1137\/1.9780898717075"},{"issue":"06","key":"187_CR7","doi-asserted-by":"crossref","first-page":"515","DOI":"10.2118\/3516-PA","volume":"12","author":"MR Todd","year":"1972","unstructured":"Todd, M.R., O\u2019dell, P.M., Hirasaki, G.J.: Methods for increased accuracy in numerical reservoir simulators. Soc. Pet. Eng. J. 12(06), 515\u2013530 (1972)","journal-title":"Soc. Pet. Eng. J."},{"issue":"1","key":"187_CR8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0021-9991(88)90065-4","volume":"74","author":"JB Bell","year":"1988","unstructured":"Bell, J.B., Dawson, C.N., Shubin, G.R.: An unsplit, higher order godunov method for scalar conservation laws in multiple dimensions. J. Comput. Phys. 74(1), 1\u201324 (1988)","journal-title":"J. Comput. Phys."},{"key":"187_CR9","unstructured":"Peaceman, D.W.: Streamline diffusion methods for problems in fluid mechanics. In: Finite Element in Fluids VI. Wiley, New York (1986)"},{"issue":"231","key":"187_CR10","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1090\/S0025-5718-99-01172-2","volume":"69","author":"DP Yang","year":"2000","unstructured":"Yang, D.P.: Analysis of least-squares mixed finite element methods for nonlinear nonstationary convection-diffusion problems. Math. Comput. 69(231), 929\u2013963 (2000)","journal-title":"Math. Comput."},{"issue":"6","key":"187_CR11","doi-asserted-by":"crossref","first-page":"1487","DOI":"10.1137\/0726087","volume":"26","author":"CN Dawson","year":"1989","unstructured":"Dawson, C.N., Russell, T.F., Wheeler, M.F.: Some improved error estimates for the modified method of characteristics. SIAM J. Numer. Anal. 26(6), 1487\u20131512 (1989)","journal-title":"SIAM J. Numer. Anal."},{"issue":"4","key":"187_CR12","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/0309-1708(90)90041-2","volume":"13","author":"MA Celia","year":"1990","unstructured":"Celia, M.A., Russell, T.F., Herrera, I., Ewing, R.E.: An eulerian-lagrangian localized adjoint method for the advection-diffusion equation. Adv. Water Resour. 13(4), 187\u2013206 (1990)","journal-title":"Adv. Water Resour."},{"issue":"138","key":"187_CR13","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1090\/S0025-5718-1977-0431719-X","volume":"31","author":"A Brandt","year":"1977","unstructured":"Brandt, A.: Multi-level adaptive solutions to boundary-value problems. Math. Comput. 31(138), 333\u2013390 (1977)","journal-title":"Math. Comput."},{"key":"187_CR14","doi-asserted-by":"crossref","unstructured":"Hackbusch, W.: Multi-Grid Methods and Applications. Springer Series in Computational Mathematics, vol 4. Springer, New York (1985)","DOI":"10.1007\/978-3-662-02427-0"},{"key":"187_CR15","doi-asserted-by":"crossref","unstructured":"Briggs, W.L., Henson, V.E., McCormick, S.F.: A Multigrid Tutorial, 2nd edn. SIAM, Philadelphia, PA (2000)","DOI":"10.1137\/1.9780898719505"},{"key":"187_CR16","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1137\/0915016","volume":"15","author":"JC Xu","year":"1994","unstructured":"Xu, J.C.: A novel two-grid method for semilinear equations. SIAM J. Sci. Comput. 15, 231\u2013237 (1994)","journal-title":"SIAM J. Sci. Comput."},{"key":"187_CR17","doi-asserted-by":"crossref","first-page":"1759","DOI":"10.1137\/S0036142992232949","volume":"33","author":"JC Xu","year":"1996","unstructured":"Xu, J.C.: Two-grid discretization techniques for linear and non-linear pdes. SIAM J. Numer. Anal. 33, 1759\u20131777 (1996)","journal-title":"SIAM J. Numer. Anal."},{"key":"187_CR18","unstructured":"Edwards, M.G., Rogers, C.F.: Multigrid and renormalization for reservoir simulation. In: Hemker, P.W., Wesseling, P. (eds.) Proceedings of the Fourth European Multigrid Conference, Amsterdam, 1993 (Birkh\u00e4user, Basel, 1994), pp. 189\u2013200"},{"issue":"1","key":"187_CR19","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1023\/B:TIPM.0000007309.48913.d2","volume":"55","author":"P Audigane","year":"2004","unstructured":"Audigane, P., Blunt, M.J.: Dual mesh method for upscaling in waterflood simulation. Transp. Porous Media 55(1), 71\u201389 (2004)","journal-title":"Transp. Porous Media"},{"key":"187_CR20","doi-asserted-by":"crossref","unstructured":"Audigane, P., Blunt, M.J.: Dual mesh method in upscaling. In: SPE Reservoir Simulation Symposium (2003)","DOI":"10.2118\/79681-MS"},{"key":"187_CR21","doi-asserted-by":"crossref","unstructured":"Verdiere, S., Gu\u00e9rillot, D., Thomas, J.M.: Dual mesh method for multiphase flows in heterogeneous porous media. In: 5th European Conference on the Mathematics of Oil Recovery (1996)","DOI":"10.3997\/2214-4609.201406903"},{"issue":"2","key":"187_CR22","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1002\/nme.668","volume":"57","author":"YP Chen","year":"2003","unstructured":"Chen, Y.P., Huang, Y.Q., Yu, D.H.: A two-grid method for expanded mixed finite-element solution of semilinear reaction-diffusion equations. Int. J. Numer. Methods Eng. 57(2), 193\u2013209 (2003)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"2","key":"187_CR23","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1002\/nme.1775","volume":"69","author":"YP Chen","year":"2007","unstructured":"Chen, Y.P., Liu, H.W., Liu, S.: Analysis of two-grid methods for reaction-diffusion equations by expanded mixed finite element methods. Int. J. Numer. Methods Eng. 69(2), 408\u2013422 (2007)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"6","key":"187_CR24","doi-asserted-by":"crossref","first-page":"830","DOI":"10.4208\/aamm.09-m09S09","volume":"1","author":"YP Chen","year":"2009","unstructured":"Chen, Y.P., Luan, P., Lu, Z.L.: Analysis of two-grid methods for nonlinear parabolic equations by expanded mixed finite element methods. Adv. Appl. Math. Mech. 1(6), 830\u2013844 (2009)","journal-title":"Adv. Appl. Math. Mech."},{"issue":"3","key":"187_CR25","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1007\/s10915-011-9469-3","volume":"49","author":"LP Chen","year":"2011","unstructured":"Chen, L.P., Chen, Y.P.: Two-grid method for nonlinear reaction-diffusion equations by mixed finite element methods. J. Sci. Comput. 49(3), 383\u2013401 (2011)","journal-title":"J. Sci. Comput."},{"issue":"02","key":"187_CR26","doi-asserted-by":"crossref","first-page":"203","DOI":"10.4208\/aamm.12-m12130","volume":"6","author":"LP Chen","year":"2014","unstructured":"Chen, L.P., Chen, Y.P.: Two-grid discretization scheme for nonlinear reaction diffusion equation by mixed finite element methods. Adv. Appl. Math. Mech. 6(02), 203\u2013219 (2014)","journal-title":"Adv. Appl. Math. Mech."},{"issue":"2","key":"187_CR27","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1137\/0732017","volume":"32","author":"T Arbogast","year":"1995","unstructured":"Arbogast, T., Wheeler, M.F.: A characteristics-mixed finite element method for advection-dominated transport problems. SIAM J. Numer. Anal. 32(2), 404\u2013424 (1995)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"187_CR28","doi-asserted-by":"crossref","first-page":"828","DOI":"10.1137\/S0036142994262585","volume":"34","author":"T Arbogast","year":"1997","unstructured":"Arbogast, T., Wheeler, M.F., Yotov, I.: Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences. SIAM J. Numer. Anal. 34(2), 828\u2013852 (1997)","journal-title":"SIAM J. Numer. Anal."},{"issue":"4","key":"187_CR29","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1002\/fld.1586","volume":"57","author":"MG Edwards","year":"2008","unstructured":"Edwards, M.G., Pal, M.: Positive-definite q-families of continuous subcell darcy-flux CVD (MPFA) finite-volume schemes and the mixed finite element method. Int. J. Numer. Methods Fluids 57(4), 355\u2013387 (2008)","journal-title":"Int. J. Numer. Methods Fluids"},{"issue":"3","key":"187_CR30","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1007\/s10915-009-9283-3","volume":"43","author":"HX Rui","year":"2010","unstructured":"Rui, H.X., Tabata, M.: A mass-conservative characteristic finite element scheme for convection-diffusion problems. J. Sci. Comput. 43(3), 416\u2013432 (2010)","journal-title":"J. Sci. Comput."},{"issue":"6","key":"187_CR31","doi-asserted-by":"crossref","first-page":"1971","DOI":"10.1002\/num.21975","volume":"31","author":"QL Deng","year":"2015","unstructured":"Deng, Q.L., Ginting, V.: Construction of locally conservative fluxes for the SUPG method. Numer. Methods Partial Differ. Equ. 31(6), 1971\u20131994 (2015)","journal-title":"Numer. Methods Partial Differ. Equ."},{"key":"187_CR32","first-page":"299","volume":"12","author":"YR Yuan","year":"1999","unstructured":"Yuan, Y.R.: Characteristic finite difference methods for positive semidefinite problem of two phase miscible flow in porous media. Syst. Sci. Math. Sci. 12, 299\u2013306 (1999)","journal-title":"Syst. Sci. Math. Sci."},{"key":"187_CR33","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1016\/j.cam.2008.09.029","volume":"228","author":"TJ Sun","year":"2009","unstructured":"Sun, T.J., Yuan, Y.R.: An approximation of incompressiblle miscible displacement in porous media by mixed finite element method and characteristics-mixed finite element methods. J. Comput. Appl. Math. 228, 391\u2013411 (2009)","journal-title":"J. Comput. Appl. Math."},{"issue":"1","key":"187_CR34","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/0045-7825(84)90048-3","volume":"47","author":"RE Ewing","year":"1984","unstructured":"Ewing, R.E., Russell, T.F., Wheeler, M.F.: Convergence analysis of an approximation of miscible displacement in porous media by mixed finite elements and a modified method of characteristics. Comput. Methods Appl. Mech. Eng. 47(1), 73\u201392 (1984)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"187_CR35","doi-asserted-by":"crossref","unstructured":"Raviart, J.M., Thomas, P.A.: A mixed finite element method for second order elliptic problems. In: Mathematical Aspects of the Finite Element Method, Lecture Notes in Mathematics, vol 606. Springer, New York (1977)","DOI":"10.1007\/BFb0064470"},{"issue":"2","key":"187_CR36","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/BF01389710","volume":"47","author":"F Brezzi","year":"1985","unstructured":"Brezzi, F., Douglas Jr., J., Marini, L.D.: Two families of mixed finite elements for second order elliptic problems. Numer. Math. 47(2), 217\u2013235 (1985)","journal-title":"Numer. Math."},{"issue":"2","key":"187_CR37","first-page":"129","volume":"8","author":"F Brezzi","year":"1974","unstructured":"Brezzi, F.: On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers. RAIRO Anal. Numer. 8(2), 129\u2013151 (1974)","journal-title":"RAIRO Anal. Numer."},{"key":"187_CR38","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1137\/0717029","volume":"17","author":"RE Ewing","year":"1980","unstructured":"Ewing, R.E., Wheeler, M.F.: Galerkin methods for miscible displacement problems in porous media. SIAM J. Numer. Anal. 17, 351\u2013365 (1980)","journal-title":"SIAM J. Numer. Anal."},{"key":"187_CR39","volume-title":"The Mathematical Theory of Finite Element Methods,Second edition. Texts in Applied Mathematics","author":"SC Susanne","year":"2002","unstructured":"Susanne, S.C., Brenner, L.R.: The Mathematical Theory of Finite Element Methods,Second edition. Texts in Applied Mathematics. Springer, New York (2002)"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0187-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-016-0187-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0187-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,16]],"date-time":"2020-05-16T15:09:49Z","timestamp":1589641789000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-016-0187-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3,5]]},"references-count":39,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,10]]}},"alternative-id":["187"],"URL":"https:\/\/doi.org\/10.1007\/s10915-016-0187-8","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,3,5]]}}}