{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,10]],"date-time":"2025-05-10T20:05:08Z","timestamp":1746907508407},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2023,1,18]],"date-time":"2023-01-18T00:00:00Z","timestamp":1674000000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,18]],"date-time":"2023-01-18T00:00:00Z","timestamp":1674000000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11801293"],"award-info":[{"award-number":["11801293"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2020MA049"],"award-info":[{"award-number":["ZR2020MA049"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2023,8]]},"DOI":"10.1007\/s11075-022-01489-3","type":"journal-article","created":{"date-parts":[[2023,1,18]],"date-time":"2023-01-18T03:34:12Z","timestamp":1674012852000},"page":"1795-1810","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A multipoint flux mixed finite element method with mass-conservative characteristic finite element method for incompressible miscible displacement problem"],"prefix":"10.1007","volume":"93","author":[{"given":"Xindong","family":"Li","sequence":"first","affiliation":[]},{"given":"Mingyang","family":"Du","sequence":"additional","affiliation":[]},{"given":"Wenwen","family":"Xu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,1,18]]},"reference":[{"key":"1489_CR1","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1016\/0045-7825(84)90048-3","volume":"47","author":"R Ewing","year":"1984","unstructured":"Ewing, R., Russell, T., 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. Engrg. 47, 73\u201392 (1984)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"1489_CR2","doi-asserted-by":"publisher","first-page":"970","DOI":"10.1137\/0722059","volume":"22","author":"T Russell","year":"1985","unstructured":"Russell, T.: Time stepping along characteristics with incomplete iteration for a Galerkin approximation of miscible displacement in porous media. SIAM J. Numer. Anal. 22, 970\u20131013 (1985)","journal-title":"SIAM J. Numer. Anal."},{"key":"1489_CR3","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1137\/0717029","volume":"17","author":"R Ewing","year":"1980","unstructured":"Ewing, R., 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":"1489_CR4","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1051\/m2an\/1983170100171","volume":"17","author":"Jr Douglas","year":"1983","unstructured":"Douglas, Jr., Ewing, R., Wheeler, M.F.: The approximation of the pressure by a mixed method in the simulation of miscible displacement. RAIRO Anal. Numer. 17, 17\u201333 (1983)","journal-title":"RAIRO Anal. Numer."},{"key":"1489_CR5","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1051\/m2an\/1983170302491","volume":"17","author":"Jr Douglas","year":"1983","unstructured":"Douglas, Jr., Ewing, R., Wheeler, M.F.: A time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media. RAIRO Anal. Numer. 17, 249\u2013265 (1983)","journal-title":"RAIRO Anal. Numer."},{"key":"1489_CR6","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1137\/S1064827598349215","volume":"22","author":"H Wang","year":"2000","unstructured":"Wang, H., Liang, D., Ewing, R.E.: An approximation to miscible fluid flows in porous media with point sources and sinks by an Eulerian-Lagrangian localized adjoint method and mixed finite element methods. SIAM J. Sci. Comput. 22, 561\u2013581 (2000)","journal-title":"SIAM J. Sci. Comput."},{"key":"1489_CR7","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/j.cma.2014.10.048","volume":"292","author":"J Li","year":"2015","unstructured":"Li, J., Riviere, B.: Numerical solutions of the incompressible miscible displacement equations in heterogeneous media. Comput. Methods Appl. Mech. Eng. 292, 107\u2013121 (2015)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"1489_CR8","first-page":"259","volume":"315","author":"W Xu","year":"2017","unstructured":"Xu, W., Liang, D., Rui, H.: A multipoint flux mixed finite element method for the compressible Darcy-Forchheimer models. Appl. Math. Comput. 315, 259\u2013277 (2017)","journal-title":"Appl. Math. Comput."},{"key":"1489_CR9","doi-asserted-by":"publisher","first-page":"1503","DOI":"10.4208\/cicp.scpde14.46s","volume":"19","author":"Y Chen","year":"2016","unstructured":"Chen, Y., Hu, H.: Two-grid method for miscible displacement problem by mixed finite element methods and mixed finite element method of characteristics. Commun. Comput. Phys. 19, 1503\u20131528 (2016)","journal-title":"Commun. Comput. Phys."},{"key":"1489_CR10","doi-asserted-by":"publisher","first-page":"611","DOI":"10.1007\/s11075-021-01127-4","volume":"89","author":"H Hu","year":"2021","unstructured":"Hu, H.: Two-grid method for compressible miscible displacement problem by mixed finite element methods and expanded mixed finite element method of characteristics. Numer. Algorithm. 89, 611\u2013636 (2021)","journal-title":"Numer. Algorithm."},{"key":"1489_CR11","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/j.jcp.2016.10.072","volume":"331","author":"S Lee","year":"2017","unstructured":"Lee, S., Wheeler, M.: Adaptive enriched Galerkin methods for miscible displacement problems with entropy residual stabilization. J. Comput. Phys. 331, 19\u201337 (2017)","journal-title":"J. Comput. Phys."},{"key":"1489_CR12","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/BF01389710","volume":"88","author":"F Brezzi","year":"1985","unstructured":"Brezzi, F., Douglas, Jr., Marini, L.: Two families of mixed finite elements for second order elliptic problems. Numer. Math. 88, 217\u2013235 (1985)","journal-title":"Numer. Math."},{"key":"1489_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-3172-1","volume-title":"Mixed and Hybrid Finite Element Methods Springer Series in Computational Mathematics, vol. 15","author":"F Brezzi","year":"1991","unstructured":"Brezzi, F., Fortin, M.: Mixed and Hybrid Finite Element Methods Springer Series in Computational Mathematics, vol. 15. Springer, Berlin (1991)"},{"key":"1489_CR14","doi-asserted-by":"publisher","first-page":"2082","DOI":"10.1137\/050638473","volume":"44","author":"M Wheeler","year":"2006","unstructured":"Wheeler, M., Yotov, I.: A multipoint flux mixed finite element method. SIAM J. Numer. Anal. 44, 2082\u20132106 (2006)","journal-title":"SIAM J. Numer. Anal."},{"key":"1489_CR15","first-page":"66","volume":"235","author":"W Xu","year":"2014","unstructured":"Xu, W.: Cell-centered finite difference method for parabolic equation. Appl. Math. Comput. 235, 66\u201379 (2014)","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"1489_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10915-019-01103-0","volume":"82","author":"W Xu","year":"2020","unstructured":"Xu, W., Liang, D., Rui, H., Li, X.: A multipoint flux mixed finite element method for Darcy-Forchheimer incompressible miscible displacement problem. J. Sci. Comput. 82(1), 1\u201320 (2020)","journal-title":"J. Sci. Comput."},{"key":"1489_CR17","first-page":"259","volume":"315","author":"W Xu","year":"2017","unstructured":"Xu, W., Liang, D., Rui, H.: A multipoint flux mixed finite element method for the compressible Darcy-Forchheimer models. Appl. Math. Comput. 315, 259\u2013277 (2017)","journal-title":"Appl. Math. Comput."},{"key":"1489_CR18","doi-asserted-by":"publisher","first-page":"871","DOI":"10.1137\/0719063","volume":"19","author":"Jr Douglas","year":"1982","unstructured":"Douglas, Jr., Russell, T.: Numerical methods for convection-dominated diffusion problems based on combining the method of characteristic with finite element of finite difference procedures. SIAM J. Numer. Anal. 19, 871\u2013885 (1982)","journal-title":"SIAM J. Numer. Anal."},{"issue":"45-48","key":"1489_CR19","doi-asserted-by":"publisher","first-page":"3862","DOI":"10.1016\/j.cma.2008.03.013","volume":"197","author":"H Rui","year":"2008","unstructured":"Rui, H.: A conservative characteristic finite volume element method for solution of the advection-diffusion equation. Comput. Methods Appl. Mech. Engrg. 197(45-48), 3862\u20133869 (2008)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"1489_CR20","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1007\/s10915-009-9283-3","volume":"43","author":"H Rui","year":"2010","unstructured":"Rui, H., Tabata, M.: A mass-conservative finite element scheme for convection-diffusion problems. J. Sci. Comput. 43, 416\u2013432 (2010)","journal-title":"J. Sci. Comput."},{"key":"1489_CR21","doi-asserted-by":"publisher","first-page":"750","DOI":"10.1016\/j.camwa.2015.05.018","volume":"70","author":"X Li","year":"2015","unstructured":"Li, X., Rui, H.: A MCC finite element approximation of incompressible miscible displacement in porous media. Comput. Math. Appl. 70, 750\u2013764 (2015)","journal-title":"Comput. Math. Appl."},{"key":"1489_CR22","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1016\/j.cam.2016.01.052","volume":"302","author":"X Li","year":"2016","unstructured":"Li, X., Rui, H., Xu, W.: A new MCC-MFE method for compressible miscible displacement in porous media. J. Comput. Appl. Math. 302, 139\u2013156 (2016)","journal-title":"J. Comput. Appl. Math."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-022-01489-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-022-01489-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-022-01489-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,22]],"date-time":"2023-07-22T09:07:47Z","timestamp":1690016867000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-022-01489-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,18]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,8]]}},"alternative-id":["1489"],"URL":"https:\/\/doi.org\/10.1007\/s11075-022-01489-3","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,18]]},"assertion":[{"value":"13 February 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 December 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 January 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"<!--Emphasis Type='Bold' removed-->Conflict of interest"}}]}}