{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T09:07:35Z","timestamp":1790672855706,"version":"4.1.0"},"reference-count":13,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>In this paper, we present two stable rectangular nonconforming mixed finite element methods for the equations of linear elasticity in two space dimensions which produce direct approximations for the stress and displacement. In the first method, the normal stress space of the matrix-valued stress space is taken as the second order rotated Brezzi\u2013Douglas\u2013Fortin\u2013Marini element space [F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991], the enriched nonconforming rotated $Q_1$ element [Q. Lin, L. Tobiska, and A. H. Zhou, IMA J. Numer. Anal., 25 (2005), pp. 160\u2013181] is taken for the shear stress, and the lowest order Raviart\u2013Thomas element space [P. A. Raviart and J. M. Thomas, in Mathematical Aspects of the Finite Element Method, Lecture Notes in Math. 606, Springer-Verlag, New York, 1977, pp. 292\u2013315] is employed to approximate the vector displacement field. The second method is obtained from the first one through dropping the interior degrees of the normal stress on each element. A first order convergence rate is obtained for both the stress and the displacement for these methods based on the superconvergence of the enriched nonconforming rotated $Q_1$ element.<\/jats:p>","DOI":"10.1137\/060669681","type":"journal-article","created":{"date-parts":[[2007,12,19]],"date-time":"2007-12-19T10:25:56Z","timestamp":1198059956000},"page":"88-102","source":"Crossref","is-referenced-by-count":45,"title":["Lower Order Rectangular Nonconforming Mixed Finite Elements for Plane Elasticity"],"prefix":"10.1137","volume":"46","author":[{"given":"Jun","family":"Hu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhong-Ci","family":"Shi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2007,12,19]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202505000741"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/s002110100348"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202503002507"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"F. Brezzi and M. Fortin,\n                      Mixed and Hybrid Finite Element Methods\n                      , Springer-Verlag, New York, 1991.","DOI":"10.1007\/978-1-4612-3172-1"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"P. G. Ciarlet,\n                      The Finite Element Method for Elliptic Problems\n                      , North-Holland, Amsterdam, 1978.","DOI":"10.1115\/1.3424474"},{"key":"R6","unstructured":"J. Hu,\n                      Quadrilateral Locking Free Elements in Elasticity\n                      , Doctorate dissertation, Institute of Computaional Mathematics, Chinese Academy of Sciences, Beijing, 2004 (in Chinese)."},{"key":"R7","first-page":"561","volume":"23","author":"Hu J.","year":"2005","journal-title":"J. Comput. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0254-9409","issn-type":"print"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"J. Hu and Z. C. Shi,\n                      Analysis of Nonconforming Quadrilateral Rotated $Q_1$ Element for Reissner-Mindlin Plate\n                      , Preprint 2003-10, Institute of Computational Mathematics, Chinese Academy of Science, 2003.","DOI":"10.1142\/9789812838766_0006"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drh008"},{"key":"R10","unstructured":"P. B. Ming,\n                      Nonconforming Finite Element vs. Locking Problem\n                      , Doctorate dissertation, Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing, 1999 (in Chinese)."},{"key":"R11","doi-asserted-by":"crossref","unstructured":"P. A. Raviart and J. M. Thomas,\n                      A mixed finite element method for second order elliptic problems\n                      , in Mathematical Aspects of the Finite Element Method, Lecture Notes in Math. 606, I. Galligani and E. Magenes, eds., Springer-Verlag, New York, 1977, pp. 292\u2013315.","DOI":"10.1007\/BFb0064470"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1007\/s10092-005-0101-5"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202506001431"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/060669681","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:09:07Z","timestamp":1787324947000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/060669681"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,12,19]]},"references-count":13,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/060669681"],"URL":"https:\/\/doi.org\/10.1137\/060669681","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,12,19]]}}}