{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T16:04:44Z","timestamp":1781280284921,"version":"3.54.1"},"reference-count":35,"publisher":"Walter de Gruyter GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this work we present and analyze a finite element scheme yielding discontinuous Galerkin approximations to the solutions of the stationary Boussinesq system for the simulation of non-isothermal flow phenomena. The model consists of a Navier\u2013Stokes-type system, describing the velocity and the pressure of the fluid, coupled to an advection-diffusion equation for the temperature. The proposed numerical scheme is based on the standard interior penalty technique and an upwind approach for the nonlinear convective terms and employs the divergence-conforming Brezzi\u2013Douglas\u2013Marini (BDM) elements of order <jats:italic>k<\/jats:italic> for the velocity, discontinuous elements of order <jats:inline-formula id=\"j_cmam-2022-0021_ineq_9999\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>k<\/m:mi>\n                              <m:mo>-<\/m:mo>\n                              <m:mn>1<\/m:mn>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2022-0021_eq_0709.png\"\/>\n                        <jats:tex-math>{k-1}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> for the pressure and discontinuous elements of order <jats:italic>k<\/jats:italic> for the temperature. Existence and uniqueness results are shown and stated rigorously for both the continuous problem and the discrete scheme, and optimal a priori error estimates are also derived. Numerical examples back up the theoretical expected convergence rates as well as the performance of the proposed technique.<\/jats:p>","DOI":"10.1515\/cmam-2022-0021","type":"journal-article","created":{"date-parts":[[2022,7,21]],"date-time":"2022-07-21T16:45:51Z","timestamp":1658421951000},"page":"797-820","source":"Crossref","is-referenced-by-count":5,"title":["A Discontinuous Galerkin Method for the Stationary Boussinesq System"],"prefix":"10.1515","volume":"22","author":[{"given":"Eligio","family":"Colmenares","sequence":"first","affiliation":[{"name":"Departamento de Ciencias B\u00e1sicas , Facultad de Ciencias , Universidad del B\u00edo-B\u00edo , Campus Fernando May , Chill\u00e1n , Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ricardo","family":"Oyarz\u00faa","sequence":"additional","affiliation":[{"name":"GIMNAP-Departamento de Matem\u00e1tica , Universidad del B\u00edo-B\u00edo , Casilla 5-C; and CI2MA, Universidad de Concepci\u00f3n, Casilla 160-C , Concepci\u00f3n , Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francisco","family":"Pi\u00f1a","sequence":"additional","affiliation":[{"name":"GIMNAP-Departamento de Matem\u00e1tica , Universidad del B\u00edo-B\u00edo , Casilla 5-C , Concepci\u00f3n , Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","published-online":{"date-parts":[[2022,7,22]]},"reference":[{"key":"2023033113381552645_j_cmam-2022-0021_ref_001","unstructured":"R. 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