{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T08:50:07Z","timestamp":1789721407457,"version":"4.0.1"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2015,6,26]],"date-time":"2015-06-26T00:00:00Z","timestamp":1435276800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"National Natural Science Foundation of Yunnan  Provincial","award":["2012FD054"],"award-info":[{"award-number":["2012FD054"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2016,4]]},"DOI":"10.1007\/s11075-015-0018-2","type":"journal-article","created":{"date-parts":[[2016,3,30]],"date-time":"2016-03-30T01:31:16Z","timestamp":1459301476000},"page":"715-727","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Cascadic multigrid methods combined with sixth order compact scheme for poisson equation"],"prefix":"10.1007","volume":"71","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4183-2404","authenticated-orcid":false,"given":"Li","family":"Ming","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Li","family":"Chen-liang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cui","family":"Xiang-zhao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhao","family":"Jin-e","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2015,6,26]]},"reference":[{"key":"18_CR1","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1090\/conm\/180\/01954","volume":"180","author":"P Deuflhard","year":"1994","unstructured":"Deuflhard, P.: Cascadic Conjugate Gradient Methods for Elliptic Partial Differential Equations: Algorithm and Numerical Results. Contemp. Math. 180, 29\u201342 (1994)","journal-title":"Contemp. Math."},{"key":"18_CR2","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/s002110050234","volume":"75","author":"F Bornemann","year":"1996","unstructured":"Bornemann, F., Deufhard, P.: The cascadic multigrid method for elliptic problems. Numer. Math. 75, 135\u2013152 (1996)","journal-title":"Numer. Math."},{"key":"18_CR3","volume-title":"The Eighth International Conference on Domain Decomposition Mehtods for Partial Differential Equations","author":"F Bornemann","year":"1997","unstructured":"Bornemann, F., Deuflhard, P.: The cascadic multigrid method. In: Glowinski, R., Periaux, J., Shi, Z.C., Widlund, O. (eds.) The Eighth International Conference on Domain Decomposition Mehtods for Partial Differential Equations. Wiley, New York (1997)"},{"key":"18_CR4","first-page":"309","volume":"6","author":"ZC Shi","year":"1998","unstructured":"Shi, Z.C., Xu, X.J.: Cascadic multigrid method for the second order elliptic problem. East-West J. Numer. Math. 6, 309\u2013318 (1998). 7: 199\u2013209 (1999)","journal-title":"East-West J. Numer. Math."},{"issue":"1","key":"18_CR5","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/BF02872279","volume":"44","author":"ZC Shi","year":"2001","unstructured":"Shi, Z.C., Xu, X.J.: A new cascadic multigrid. Sci. China Ser. A-Math. 44 (1), 21\u201330 (2001)","journal-title":"Sci. China Ser. A-Math."},{"key":"18_CR6","doi-asserted-by":"publisher","first-page":"1765","DOI":"10.1007\/s11425-007-0127-z","volume":"50","author":"ZC Shi","year":"2007","unstructured":"Shi, Z.C., Xu, X.J., Huang, YQ.: Economical cascadic multigrid methods (ECMG). Sci. China Ser. A-Math. 50, 1765\u20131780 (2007)","journal-title":"Sci. China Ser. A-Math."},{"key":"18_CR7","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1007\/BF01389427","volume":"49","author":"H Blum","year":"1986","unstructured":"Blum, H., Lin, Q., Rannacher, R.: Asymptotic Error Expansion and Richardson Extrapolation for Linear Finite Elements. Numer. Math. 49, 11\u201337 (1986)","journal-title":"Numer. Math."},{"key":"18_CR8","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1007\/BF01400891","volume":"52","author":"H Blum","year":"1988","unstructured":"Blum, H., Rannacher, R.: Extrapolation Techniques for Reducing the Pollution Effect of Reentrant Corners in the Finite Element Method. Numer. Math. 52, 539\u2013564 (1988)","journal-title":"Numer. Math."},{"key":"18_CR9","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1063\/1.2751928","volume":"29","author":"CL Li","year":"2007","unstructured":"Li, C.L., Chen, C.M., Xu, XJ.: A cascadicmultigrid method based on superconvergence and extrapolation. Numer. Math. Sinica. 29, 439\u2013448 (2007)","journal-title":"Numer. Math. Sinica."},{"issue":"2","key":"18_CR10","first-page":"1","volume":"30","author":"CM Chen","year":"2007","unstructured":"Chen, C.M., Xie, Z.Q., Li, C.L., et al.: Study of a new extrapolation multigrid method (in English). Natur. Numer. Sci. J. Hunan. Normal. Univ. 30(2), 1\u20135 (2007)","journal-title":"Natur. Numer. Sci. J. Hunan. Normal. Univ."},{"issue":"8","key":"18_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11431-008-0002-3","volume":"51","author":"CM Chen","year":"2008","unstructured":"Chen, C.M., Hu, H.L., Xie, Z.Q., et al.: Analysis of extrapolation cascadic multigrid method (EXCMG). Sci. China ser. A-Math. 51(8), 1\u201312 (2008)","journal-title":"Sci. China ser. A-Math."},{"issue":"3","key":"18_CR12","first-page":"539","volume":"29B","author":"CM Chen","year":"2009","unstructured":"Chen, C.M., Hu, H.L., Xie, Z.Q., et al.: L\n                           2-error of extrapolation cascadic multigrid (EXCMG). Acta. Math. Sci. 29B(3), 539\u2013551 (2009)","journal-title":"Acta. Math. Sci."},{"issue":"3","key":"18_CR13","first-page":"261","volume":"31","author":"HL Hu","year":"2009","unstructured":"Hu, H.L., Chen, C.M., Xie, Z.Q.: Extrapolation cascadic multigrid method (EXCMG)\u2013a new algorithm for solving large scale ellliptic problems. Numer. Math. Sinica. 31(3), 261\u2013274 (2009)","journal-title":"Numer. Math. Sinica."},{"issue":"2","key":"18_CR14","first-page":"109","volume":"26","author":"ZF Tian","year":"1996","unstructured":"Tian, Z.F.: Compact high-order difference methods for solving the Poisson equation. Journal of Northwest Universtity (Natural Science Edition) 26(2), 109\u2013114 (1996)","journal-title":"Journal of Northwest Universtity (Natural Science Edition)"},{"key":"18_CR15","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1006\/jcph.2002.7049","volume":"179","author":"J Zhang","year":"2002","unstructured":"Zhang, J.: Multigrid method and fourth order compact difference scheme for 2D Poisson equation with unequal meshsize discretization. Comput. Phys. 179, 170\u2013179 (2002)","journal-title":"Comput. Phys."},{"key":"18_CR16","volume-title":"Mathematical Theory of Finite Element Methods","author":"LH Wang","year":"2004","unstructured":"Wang, L.H., Xue, X.J.: Mathematical Theory of Finite Element Methods. Science press, Beijin (2004)"},{"key":"18_CR17","volume-title":"Multi-grid Methods and Applications","author":"W Hackbusch","year":"2003","unstructured":"Hackbusch, W.: Multi-grid Methods and Applications. Springer, Berlin (2003)"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-015-0018-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-015-0018-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-015-0018-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-015-0018-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,3,3]],"date-time":"2020-03-03T07:25:56Z","timestamp":1583220356000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-015-0018-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6,26]]},"references-count":17,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2016,4]]}},"alternative-id":["18"],"URL":"https:\/\/doi.org\/10.1007\/s11075-015-0018-2","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,6,26]]},"assertion":[{"value":"14 November 2014","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 June 2015","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 June 2015","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}