Title:   Preconditioning for the mixed formulation of linear plane elasticity 
Speaker: Yanqiu Wang,  Purdue University


Abstract: 
We study the mixed finite element method
for the linear plane elasticity problem and iterative solvers
for the resulting discrete system. The Arnold-Winther Element
is used for the mixed finite element discretization.
An overlapping Schwarz preconditioner and a multigrid preconditioner
for the discrete system are developed and analyzed.

We start by introducing the mixed formulation (stress-displacement formulation)
for the linear plane elasticity problem and its discretization.
A brief description of the Arnold-Winther Element is given.
The finite element discretization of the mixed formulation
leads to a symmetric indefinite linear system.

To solve the mixed system, the preconditioned Minimum Residual Method
is considered.  It can be shown that the problem of constructing a
preconditioner for the indefinite linear system can be reduced to the
problem of constructing a preconditioner for the H(div) problem in the
Arnold-Winther finite element space.  Our main work involves
developing an overlapping Schwarz preconditioner and a multigrid
preconditioner for the H(div) problem.  We give condition number
estimates for the preconditioned systems together with supporting
numerical results.


PS: This is my research for the Ph.D. dissertation in Texas A&M
University.  I would like to thank my advisor, Dr. Joseph Pasciak for
his direction and help.