A Preconditioning Technique for Indefinite Systems Resulting from Mixed Approximations of Elliptic Problems
- 1 January 1988
- journal article
- Published by JSTOR in Mathematics of Computation
- Vol. 50 (181) , 1-17
- https://doi.org/10.2307/2007912
Abstract
This paper provides a preconditioned iterative technique for the solution of saddle point problems. These problems typically arise in the numerical approximation of partial differential equations by Lagrange multiplier techniques and/or mixed methods. The saddle point problem is reformulated as a symmetric positive definite system, which is then solved by conjugate gradient iteration. Applications to the equations of elasticity and Stokes are discussed and the results of numerical experiments are given.Keywords
This publication has 18 references indexed in Scilit:
- The Construction of Preconditioners for Elliptic Problems by Substructuring. IIMathematics of Computation, 1987
- The Construction of Preconditioners for Elliptic Problems by Substructuring. IMathematics of Computation, 1986
- An Iterative Method for Elliptic Problems on Regions Partitioned into SubstructuresMathematics of Computation, 1986
- A boundary parametric approximation to the linearized scalar potential magnetostatic field problemApplied Numerical Mathematics, 1985
- Computer Solution of Large Sparse Positive Definite Systems.Mathematics of Computation, 1982
- The Lagrange Multiplier Method for Dirichlet's ProblemMathematics of Computation, 1981
- The Finite Element Method for Elliptic ProblemsJournal of Applied Mechanics, 1978
- An Analysis of the Finite Element Method Using Lagrange Multipliers for the Stationary Stokes EquationsMathematics of Computation, 1976
- On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliersRevue française d'automatique, informatique, recherche opérationnelle. Analyse numérique, 1974
- The finite element method with Lagrangian multipliersNumerische Mathematik, 1973