High accuracy analysis of two nonconforming plate elements

We prove the superconvergence of Morley element and the incomplete biquadratic nonconforming element for the plate bending problem. Under uniform rectangular meshes, we obtain a superconvergence property at the symmetric points of the elements and a global superconvergent result by a proper postprocessing method.

[1]  M. Zlámal,et al.  Some superconvergence results in the finite element method , 1977 .

[2]  Zhong-Ci Shi,et al.  SUPERCONVERGENCE STUDIES OF QUADRILATERAL NONCONFORMING ROTATED Q1 ELEMENTS , 2006 .

[3]  J. Z. Zhu,et al.  Superconvergence recovery technique and a posteriori error estimators , 1990 .

[4]  Shipeng Mao,et al.  A quadrilateral, anisotropic, superconvergent, nonconforming double set parameter element , 2006 .

[5]  Q. Lin,et al.  Superconvergence and extrapolation of non-conforming low order finite elements applied to the Poisson equation , 2005 .

[6]  Zhimin Zhang,et al.  Derivative superconvergent points in finite element solutions of Poisson's equation for the serendipity and intermediate families - a theoretical justification , 1998, Math. Comput..

[7]  Ivo Babuška,et al.  Computer‐based proof of the existence of superconvergence points in the finite element method; superconvergence of the derivatives in finite element solutions of Laplace's, Poisson's, and the elasticity equations , 1996 .

[8]  Jan Brandts Superconvergence and a posteriori error estimation for triangular mixed finite elements , 1994 .

[9]  Zhongci Shi The F-E-M test for convergence of nonconforming finite elements , 1987 .

[10]  Bo Li,et al.  Nonconforming finite element approximation of crystalline microstructure , 1998, Math. Comput..

[11]  Philippe G. Ciarlet,et al.  The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[12]  Zhimin Zhang,et al.  Analysis of recovery type a posteriori error estimators for mildly structured grids , 2003, Math. Comput..

[13]  Ian H. Sloan,et al.  Superconvergence in finite element methods and meshes that are locally symmetric with respect to a point , 1996 .

[14]  Jim Douglas,et al.  Superconvergence for galerkin methods for the two point boundary problem via local projections , 1973 .

[15]  Zhong-Ci Shi,et al.  A new superconvergence property of Wilson nonconforming finite element , 1997 .

[16]  Miloš Zlámal,et al.  Superconvergence and reduced integration in the finite element method , 1978 .

[18]  J. Z. Zhu,et al.  The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity , 1992 .

[19]  L. Wahlbin Superconvergence in Galerkin Finite Element Methods , 1995 .

[20]  Richard E. Ewing,et al.  Superconvergence of the velocity along the Gauss lines in mixed finite element methods , 1991 .

[21]  Shaochun Chen,et al.  Plate Elements With High Accuracy , 1997 .

[22]  J. Z. Zhu,et al.  The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique , 1992 .

[23]  Pekka Neittaanmäki,et al.  On superconvergence techniques , 1987 .

[24]  Bo Li,et al.  Superconvergence analysis and error expansion for the Wilson nonconforming finite element , 1994 .

[25]  Rolf Stenberg,et al.  Finite element methods: superconvergence, post-processing, and a posteriori estimates , 1998 .

[26]  Wang Cai-xia,et al.  Superconvergence Analysis of Nonconforming Mixed Finite Element Method for Stokes Problem , 2007 .