Xiao, Liuchao; Jiang, Yongyan; Chen, Shaochun A second-order nonconforming rectangle element for the planar elasticity with pure traction boundary condition. (Chinese. English summary) Zbl 1274.74454 Numer. Math., Nanjing 34, No. 2, 185-192 (2012). Summary: In this paper, we present a nonconforming rectangle finite element, which satisfies the discrete version of Korn’s second inequality. And the element is locking-free for the equation of elasticity with pure traction boundary condition. Furthermore, we prove the scheme is uniformly convergent with the rate of order two and three in the energy norm and \(L^2\)-norm, respectively. MSC: 74S05 Finite element methods applied to problems in solid mechanics 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs Keywords:planar elasticity; pure traction boundary condition; nonconforming finite element; Korn’s second inequality PDFBibTeX XMLCite \textit{L. Xiao} et al., Numer. Math., Nanjing 34, No. 2, 185--192 (2012; Zbl 1274.74454)