{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T23:40:25Z","timestamp":1776728425773,"version":"3.51.2"},"reference-count":22,"publisher":"American Mathematical Society (AMS)","issue":"240","license":[{"start":{"date-parts":[[2002,12,5]],"date-time":"2002-12-05T00:00:00Z","timestamp":1039046400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>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.<\/p>","DOI":"10.1090\/s0025-5718-01-01394-1","type":"journal-article","created":{"date-parts":[[2002,9,20]],"date-time":"2002-09-20T14:12:48Z","timestamp":1032531168000},"page":"1455-1472","source":"Crossref","is-referenced-by-count":11,"title":["Conjugate gradient method for dual-dual mixed formulations"],"prefix":"10.1090","volume":"71","author":[{"given":"Gabriel","family":"Gatica","sequence":"first","affiliation":[]},{"given":"Norbert","family":"Heuer","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2001,12,5]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"828","DOI":"10.1137\/S0036142994262585","article-title":"Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences","volume":"34","author":"Arbogast, Todd","year":"1997","journal-title":"SIAM J. Numer. 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Technical Report 99-03, Departamento de Ingenier\u00eda Matem\u00e1tica, Universidad de Concepci\u00f3n, Chile. Submitted for publication. \\url{http:\/\/www.ing-mat.udec.cl\/inf-loc-dim.html}"},{"issue":"2","key":"11","doi-asserted-by":"publisher","first-page":"380","DOI":"10.1137\/S0036142999363486","article-title":"A dual-dual formulation for the coupling of mixed-FEM and BEM in hyperelasticity","volume":"38","author":"Gatica, Gabriel N.","year":"2000","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"12","doi-asserted-by":"crossref","unstructured":"G. N. Gatica and N. Heuer, Minimum residual iteration for a dual-dual mixed formulation of exterior transmission problems, Numer. Linear Algebra Appl., 8 (2001), pp. 147\u2013164.","DOI":"10.1002\/1099-1506(200104\/05)8:3<147::AID-NLA236>3.0.CO;2-2"},{"key":"13","doi-asserted-by":"crossref","unstructured":"G. N. Gatica and N. 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