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Numerical validation of solutions of saddle point matrix equations

A numerical validation method for verifying the accuracy of approximate solutions of saddle point matrix equations is presented and analysed. The method only requires iterative solutions of two symmetric positive definite linear systems. Moreover, it is shown that preconditioning can be used to improve the error bounds. The method is illustrated by several examples derived from mixed finite element discretization of the Stokes equations. Preliminary numerical results indicate that the method is efficient. Copyright © 2003 John Wiley & Sons, Ltd.