A locking-free anisotropic nonconforming rectangular finite element approximation for the planar elasticity problem

This paper deals with a new nonconforming anisotropic rectangular finite element approximation for the planar elasticity problem with pure displacement boundary condition. By use of the special properties of this element, and by introducing the complementary space and a series of novel techniques, the optimal error estimates of the energy norm and the L2-norm are obtained. The restrictions of regularity assumption and quasi-uniform assumption or the inverse assumption on the meshes required in the conventional finite element methods analysis are to be got rid of and the applicable scope of the nonconforming finite elements is extended.

[1]  Dongyang Shi,et al.  Anisotropic interpolation and quasi‐Wilson element for narrow quadrilateral meshes , 2004 .

[2]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .

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

[4]  I. Babuska,et al.  Locking effects in the finite element approximation of elasticity problems , 1992 .

[5]  Dongwoo Sheen,et al.  P1-Nonconforming Quadrilateral Finite Element Methods for Second-Order Elliptic Problems , 2003, SIAM J. Numer. Anal..

[6]  S. C. Brenner,et al.  Linear finite element methods for planar linear elasticity , 1992 .

[7]  R. Kouhia,et al.  A linear nonconforming finite element method for nearly incompressible elasticity and stokes flow , 1995 .

[8]  Ricardo G. Durán,et al.  The Maximum Angle Condition for Mixed and Nonconforming Elements: Application to the Stokes Equations , 1999, SIAM J. Numer. Anal..

[9]  R. S. Falk.  Nonconforming finite element methods for the equations of linear elasticity , 1991 .

[10]  T. Apel.  Anisotropic Finite Elements: Local Estimates and Applications , 1999 .

[11]  R. Rannacher,et al.  Simple nonconforming quadrilateral Stokes element , 1992 .

[12]  Dongwoo Sheen,et al.  A Locking-Free Nonconforming Finite Element Method for Planar Linear Elasticity , 2003, Adv. Comput. Math..

[13]  Thomas Apel,et al.  Anisotropic interpolation with applications to the finite element method , 1991, Computing.

[14]  Zhang,et al.  A Locking-free Nonconforming Finite Element for Planar Linear Elasticity , 2005 .

[15]  N. SIAMJ..  ANALYSIS OF SOME QUADRILATERAL NONCONFORMING ELEMENTS FOR INCOMPRESSIBLE ELASTICITY , 1997 .

[16]  Dongyang Shi,et al.  Anisotropic interpolations with application to nonconforming elements , 2004 .