{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T21:06:34Z","timestamp":1758402394093,"version":"3.37.3"},"reference-count":18,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11271281"],"award-info":[{"award-number":["11271281"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>We propose a fully discrete method for the multiscale Richards\u2019 equation of van Genuchten-Mualem model which describes the flow transport in unsaturated heterogenous porous media. Under the framework of heterogeneous multiscale method (HMM), a fully discrete scheme combined with a regularized procedure is proposed. Including the numerical integration, the discretization is given by<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:msup><mml:mi>C<\/mml:mi><mml:mn>0<\/mml:mn><\/mml:msup><\/mml:mrow><\/mml:math>piecewise finite element in space and an implicit scheme in time. Error estimates between the numerical solution and the solution of homogenized problem are derived under the assumption that the permeability is periodic. Numerical experiments with periodic and random permeability are carried out for the van Genuchten-Mualem model of Richards\u2019 equation to show the efficiency and accuracy of the proposed method.<\/jats:p>","DOI":"10.1155\/2014\/657816","type":"journal-article","created":{"date-parts":[[2014,3,20]],"date-time":"2014-03-20T17:03:26Z","timestamp":1395335006000},"page":"1-10","source":"Crossref","is-referenced-by-count":1,"title":["A Completely Discrete Heterogeneous Multiscale Finite Element Method for Multiscale Richards\u2019 Equation of van Genuchten-Mualem Model"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1913-4514","authenticated-orcid":true,"given":"Haitao","family":"Cao","sequence":"first","affiliation":[{"name":"Department of Mathematics and Physics, Hohai University, Changzhou Campus, Changzhou 213022, China"},{"name":"Department of Mathematics, Soochow University, Suzhou, Jiangsu 215006, China"}]},{"given":"Tao","family":"Yu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Jinggangshan University, Ji\u2019an, Jiangxi 343009, China"}]},{"given":"Xingye","family":"Yue","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Soochow University, Suzhou, Jiangsu 215006, China"}]}],"member":"311","reference":[{"key":"27","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1063\/1.1745010","volume":"1","year":"1931","journal-title":"Physics"},{"issue":"5","key":"13","doi-asserted-by":"crossref","first-page":"892","DOI":"10.2136\/sssaj1980.03615995004400050002x","volume":"44","year":"1980","journal-title":"Soil Science Society of America Journal"},{"issue":"3","key":"19","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1029\/WR012i003p00513","volume":"12","year":"1976","journal-title":"Water Resources Research"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01176474"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1007\/BF03167758"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1137\/0725046"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019936917350"},{"key":"25","first-page":"1452","volume":"4","year":"2004","journal-title":"SIAM Journal on Numerical Analysis"},{"issue":"5","key":"16","first-page":"605","volume":"29","year":"1995","journal-title":"RAIRO Mod\u00e9lisation Math\u00e9matique et Analyse Num\u00e9rique"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/S0309-1708(00)00076-2"},{"key":"24","first-page":"1365","volume":"168","year":"2004","journal-title":"Journal of Computational and Applied Mathematics"},{"issue":"5","key":"28","doi-asserted-by":"crossref","first-page":"1593","DOI":"10.1137\/S1064827500381860","volume":"23","year":"2002","journal-title":"SIAM Journal on Scientific Computing"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1997.5682"},{"key":"11","doi-asserted-by":"crossref","first-page":"87","DOI":"10.4310\/CMS.2003.v1.n1.a8","volume":"1","year":"2003","journal-title":"Communications in Mathematical Sciences"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.4310\/CMS.2005.v3.n4.a2"},{"key":"2","series-title":"GAKUTO International Series Mathematical Sciences & Applications","first-page":"133","volume-title":"The finite element heterogeneous multiscale method: a computational strategy for multiscale PDEs","volume":"31","year":"2009"},{"year":"1978","key":"9"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2013.10.063"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/657816.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/657816.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/657816.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T06:01:18Z","timestamp":1498111278000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/657816\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":18,"alternative-id":["657816","657816"],"URL":"https:\/\/doi.org\/10.1155\/2014\/657816","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}