An Optimal Preconditioner for a Class of Saddle Point Problems with a Penalty Term
- 1 January 1998
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Scientific Computing
- Vol. 19 (2) , 540-552
- https://doi.org/10.1137/s1064827595279575
Abstract
Iterative methods are considered for a class of saddle point problems with a penalty term arising from finite element discretizations of certain elliptic problems. An optimal preconditioner which is independent of the and the penalty parameter is constructed. This approach is then used to design an iterative method with a convergence rate independent of the Lam\''{e} parameters occuring in the equations of linear elasticity. Please see revised version tr683.Keywords
This publication has 27 references indexed in Scilit:
- Analysis of the Inexact Uzawa Algorithm for Saddle Point ProblemsSIAM Journal on Numerical Analysis, 1997
- A nonconforming mixed multigrid method for the pure traction problem in planar linear elasticityMathematics of Computation, 1994
- A Nonconforming Mixed Multigrid Method for the Pure Displacement Problem in Planar Linear ElasticitySIAM Journal on Numerical Analysis, 1993
- Locking effects in the finite element approximation of elasticity problemsNumerische Mathematik, 1992
- A multigrid method for a parameter dependent problem in solid mechanicsNumerische Mathematik, 1990
- A Taxonomy for Conjugate Gradient MethodsSIAM Journal on Numerical Analysis, 1990
- A class of iterative methods for solving saddle point problemsNumerische Mathematik, 1989
- A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problemsMathematics of Computation, 1988
- A multigrid method for the membrane problemComputational Mechanics, 1988
- The finite element method with Lagrangian multipliersNumerische Mathematik, 1973