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Some of the necessary estimates are straightforward modifications of well-known results, while other technical tools require a more elaborated analysis. The velocity is approximated by Raviart\u2013Thomas elements, the vorticity uses N\u00e9d\u00e9lec spaces of the first kind, the pressure is approximated by piecewise polynomials, and the temperature by continuous and piecewise polynomials of one degree higher than pressure. Special care is needed to establish discrete inf-sup conditions since the curl of the discrete vorticity is not necessarily contained in the discrete velocity space, therefore suggesting to use two different Raviart\u2013Thomas interpolants. A discrete fixed-point argument is used to show well-posedness of the Galerkin scheme. Error estimates in appropriate norms are derived, and a few representative numerical examples in 2D and 3D and with mixed boundary conditions are provided.<\/jats:p>","DOI":"10.1007\/s00211-026-01536-4","type":"journal-article","created":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T07:32:53Z","timestamp":1774078373000},"page":"1109-1149","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Numerical analysis of a porous natural convection system with vorticity and viscous dissipation"],"prefix":"10.1007","volume":"158","author":[{"given":"Russel","family":"Demos","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rashmi","family":"Dubey","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ricardo","family":"Ruiz-Baier","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Segundo","family":"Villa-Fuentes","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,3,21]]},"reference":[{"key":"1536_CR1","doi-asserted-by":"publisher","first-page":"1673","DOI":"10.1090\/S0025-5718-03-01615-6","volume":"73","author":"M Amara","year":"2004","unstructured":"Amara, M., Chac\u00f3n Vera, E., Trujillo, D.: Vorticity-velocity-pressure formulation for Stokes problem. 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