Conjugate gradient method for dual-dual mixed formulations

Gatica, Gabriel; Heuer, Norbert

doi:10.1090/S0025-5718-01-01394-1

Conjugate gradient method for dual-dual mixed formulations
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by Gabriel N. Gatica and Norbert Heuer PDF

Math. Comp. 71 (2002), 1455-1472 Request permission

Abstract:

We deal with the iterative solution of linear systems arising from so-called dual-dual mixed finite element formulations. The linear systems are of a two-fold saddle point structure; they are indefinite and ill-conditioned. We define a special inner product that makes matrices of the two-fold saddle point structure, after a specific transformation, symmetric and positive definite. Therefore, the conjugate gradient method with this special inner product can be used as iterative solver. For a model problem, we propose a preconditioner which leads to a bounded number of CG-iterations. Numerical experiments for our model problem confirming the theoretical results are also reported.

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