Jia, Shanghui; Xie, Hehu; Yin, Xiaobo; Gao, Shaoqin Approximation and eigenvalue extrapolation of biharmonic eigenvalue problem by nonconforming finite element methods. (English) Zbl 1151.65086 Numer. Methods Partial Differ. Equations 24, No. 2, 435-448 (2008). This paper deals with the eigenvalue problem \(\Delta^2 u=\lambda\rho u\) in \(\Omega\), \(u= {\partial u\over\partial n}= 0\) on \(\partial\Omega\), \(\int_\Omega\rho u^2= 1\). The authors analyze this problem by two nonconforming finite element methods and obtain a full order convergence rate of the eigenvalue approximations. Reviewer: Pavol Chocholatý (Bratislava) Cited in 14 Documents MSC: 65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 35P15 Estimates of eigenvalues in context of PDEs Keywords:asymptotic expansions; biharmonic eigenvalue problem; extrapolation; nonconforming finite element methods; convergence × Cite Format Result Cite Review PDF Full Text: DOI References: [1] and , The construction and analysis of high efficiency finite element methods (in Chinese), HeBei University Publishers, 1995. Baoding, China, 1996. [2] Multigrid methods for finite element, Kluwer Academic, Netherlands, 1995. · doi:10.1007/978-94-015-8527-9 [3] Lin, Bonner Math Schrift 158 pp 1– (1984) [4] , and , New expansion of numerical eigenvalue for - {\(\Delta\)}u = {\(\lambda\)}{\(\rho\)}u by nonconforming elements, to appear. [5] and , Finite element methods: accuracy and improvement, China Press, Beijing, 2006. [6] and , Preprocessing and postprocessing for the fininite element method (in Chinese), Shanghai Scientific and Technical Press, Shanghai, 1994. [7] Xu, Math Comput 70 pp 17– (2001) [8] Chen, Adv Comput Math [9] Chen, Numer Meth PDEs 21 pp 512– (2005) · Zbl 1073.65124 · doi:10.1002/num.20043 [10] Finite element methods and their applications, Springer–Verlag, Berlin, Heidenberg, 2005. [11] The finite element method for elliptic problem, North-Holland, Amsterdam, 1978. [12] Babuska, Math Comp 52 pp 275– (1989) [13] An analysis of the finite element method for eigenvalue problems (in Chinese), Guizhou People Public Press, Guiyang, China, 2004. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.