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We choose to demonstrate the methodology for mixed formulations, with a lowest-order Raviart\u2013Thomas\u2013N\u00e9d\u00e9lec discretization, often used for heterogeneous and anisotropic porous media diffusion problems. Our estimators allow to distinguish the spatial discretization and the domain decomposition error components. We propose an adaptive domain decomposition algorithm wherein the iterations are stopped when the domain decomposition error does not affect significantly the overall error. Two main goals are thus achieved. First, a guaranteed bound on the overall error is obtained at each step of the domain decomposition algorithm. Second, important savings in terms of the number of domain decomposition iterations can be realized. Numerical experiments illustrate the efficiency of our estimates and the performance of the adaptive stopping criteria.<\/jats:p>","DOI":"10.1515\/cmam-2018-0010","type":"journal-article","created":{"date-parts":[[2018,7,16]],"date-time":"2018-07-16T22:16:14Z","timestamp":1531779374000},"page":"495-519","source":"Crossref","is-referenced-by-count":10,"title":["A Posteriori Stopping Criteria for Optimized Schwarz Domain Decomposition Algorithms in Mixed Formulations"],"prefix":"10.1515","volume":"18","author":[{"given":"Sarah","family":"Ali Hassan","sequence":"first","affiliation":[{"name":"Inria Paris , 2 rue Simone Iff, 75589 Paris 12 ; and Universit\u00e9 Paris-Est, CERMICS (ENPC), 77455 Marne-la-Vall\u00e9e 2 , France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Caroline","family":"Japhet","sequence":"additional","affiliation":[{"name":"UMR 7539, LAGA , Universit\u00e9 Paris 13 , 93430 Villetaneuse , France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michel","family":"Kern","sequence":"additional","affiliation":[{"name":"Inria Paris , 2 rue Simone Iff, 75589 Paris 12 ; and Universit\u00e9 Paris-Est, CERMICS (ENPC), 77455 Marne-la-Vall\u00e9e 2 , France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"Vohral\u00edk","sequence":"additional","affiliation":[{"name":"Inria Paris , 2 rue Simone Iff, 75589 Paris 12 ; and Universit\u00e9 Paris-Est, CERMICS (ENPC), 77455 Marne-la-Vall\u00e9e 2 , France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2018,6,27]]},"reference":[{"key":"2023033110284041136_j_cmam-2018-0010_ref_001_w2aab3b7e4770b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"Y. 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