An auxiliary space preconditioner for linear elasticity based on the generalized finite element method

SUMMARY We construct and analyze a preconditioner of the linear elasticity system discretized by conforming linear finite elements in the framework of the auxiliary space method. The auxiliary space preconditioner is based on two auxiliary spaces corresponding to discretizations of the scalar Poisson equation by linear finite elements and the generalized finite element method. Copyright © 2011 John Wiley & Sons, Ltd.

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

[2]  I. Babuska,et al.  On locking and robustness in the finite element method , 1992 .

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

[4]  Douglas N. Arnold,et al.  Mixed finite elements for elasticity , 2002, Numerische Mathematik.

[5]  Susanne C. Brenner.  A nonconforming mixed multigrid method for the pure traction problem in planar linear elasticity , 1994 .

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

[7]  Ludmil T. Zikatanov,et al.  A multilevel preconditioning for generalized finite element method problems on unstructured simplicial meshes , 2007, J. Num. Math..

[8]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[9]  J. Pasciak,et al.  Parallel multilevel preconditioners , 1990 .

[10]  Thomas A. Manteuffel,et al.  First-Order System Least Squares For Linear Elasticity: Numerical Results , 1999, SIAM J. Sci. Comput..

[11]  Jinchao Xu,et al.  Iterative Methods by Space Decomposition and Subspace Correction , 1992, SIAM Rev..

[12]  Jinchao Xu,et al.  The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids , 1996, Computing.

[13]  Chang-Ock Lee.  A conforming mixed finite element method for the pure traction problem of linear elasticity , 1998, Appl. Math. Comput..

[14]  Joachim Schöberl,et al.  Multigrid methods for a parameter dependent problem in primal variables , 1999, Numerische Mathematik.

[15]  L. Franca,et al.  Error analysis of some Galerkin least squares methods for the elasticity equations , 1991 .

[16]  Thomas A. Manteuffel,et al.  First-Order System Least Squares (FOSLS) for Planar Linear Elasticity: Pure Traction Problem , 1998 .