{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T18:41:37Z","timestamp":1783104097576,"version":"3.54.6"},"reference-count":39,"publisher":"American Mathematical Society (AMS)","issue":"272","license":[{"start":{"date-parts":[[2011,4,21]],"date-time":"2011-04-21T00:00:00Z","timestamp":1303344000000},"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 propose a convergent implicit stabilized finite element discretization of the nonstationary incompressible magnetohydrodynamics equations with variable density, viscosity, and electric conductivity. The discretization satisfies a discrete energy law, and a discrete maximum principle for the positive density, and iterates converge to weak solutions of the limiting problem for vanishing discretization parameters. A simple fixed point scheme, together with an appropriate stopping criterion is proposed, which decouples the computation of density, velocity, and magnetic field, and inherits the above properties, provided a mild mesh constraint holds. Computational studies are provided.<\/p>","DOI":"10.1090\/s0025-5718-10-02341-0","type":"journal-article","created":{"date-parts":[[2010,7,6]],"date-time":"2010-07-06T17:17:12Z","timestamp":1278436632000},"page":"1957-1999","source":"Crossref","is-referenced-by-count":26,"title":["Convergent finite element discretization of the multi-fluid nonstationary incompressible magnetohydrodynamics equations"],"prefix":"10.1090","volume":"79","author":[{"given":"\u013dubom\u00edr","family":"Ba\u0148as","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andreas","family":"Prohl","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2010,4,21]]},"reference":[{"issue":"9","key":"1","doi-asserted-by":"publisher","first-page":"823","DOI":"10.1002\/(SICI)1099-1476(199806)21:9<823::AID-MMA976>3.0.CO;2-B","article-title":"Vector potentials in three-dimensional non-smooth domains","volume":"21","author":"Amrouche, C.","year":"1998","journal-title":"Math. 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