Conjugate gradient method for dual-dual mixed formulations
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- by Gabriel N. Gatica and Norbert Heuer PDF
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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.References
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Additional Information
- Gabriel N. Gatica
- Affiliation: GI$^2$MA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile.
- Email: ggatica@ing-mat.udec.cl
- Norbert Heuer
- Affiliation: GI$^2$MA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile.
- MR Author ID: 314970
- Email: norbert@ing-mat.udec.cl
- Received by editor(s): September 22, 1999
- Received by editor(s) in revised form: October 3, 2000
- Published electronically: December 5, 2001
- Additional Notes: This research was partially supported by CONICYT-Chile through Program A on Numerical Analysis of the FONDAP in Applied Mathematics and Fondecyt project No. 1980122, and by the Dirección de Investigación of the Universidad de Concepción through the Advanced Research Groups Program
- © Copyright 2001 American Mathematical Society
- Journal: Math. Comp. 71 (2002), 1455-1472
- MSC (2000): Primary 65N30, 65N22, 65F10
- DOI: https://doi.org/10.1090/S0025-5718-01-01394-1
- MathSciNet review: 1933040