An Optimal Preconditioner for a Class of Saddle Point Problems with a Penalty Term

Iterative methods are considered for saddle point problems with penalty term. A positive definite preconditioner is constructed and it is proved that the condition number of the preconditioned system can be made independent of the discretization and the penalty parameters. Examples include the pure displacement problem in linear elasticity, the Timoshenko beam, and the Mindlin-Reissner plate. Key words: Saddle point problems, penalty term, nearly incompressible materials, Timoshenko, Mindlin-Reissner, preconditioned conjugate residual method, multilevel, domain decomposition. Please note: This report is a revised version of tr676.