{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T11:26:42Z","timestamp":1792063602314,"version":"4.4.0"},"reference-count":48,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"name":"ANID-Subdireccion de Capital Humano\/Doctorado Nacional","award":["2020-21200920"],"award-info":[{"award-number":["2020-21200920"]}]},{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["1210729"],"award-info":[{"award-number":["1210729"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["1220156"],"award-info":[{"award-number":["1220156"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2023,10,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In Lipschitz domains, we study a Darcy\u2013Forchheimer problem coupled with a singular heat equation by a nonlinear forcing term depending on the temperature. By singular we mean that the heat source corresponds to a Dirac measure. We establish the existence of solutions for a model that allows a diffusion coefficient in the heat equation depending on the temperature. For such a model, we also propose a finite element discretization scheme and provide an a priori convergence analysis. In the case that the aforementioned diffusion coefficient is constant, we devise an a posteriori error estimator and investigate reliability and efficiency properties. We conclude by devising an adaptive loop based on the proposed error estimator and presenting numerical experiments.<\/jats:p>","DOI":"10.1137\/22m1536340","type":"journal-article","created":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T04:34:57Z","timestamp":1698208497000},"page":"A2755-A2780","source":"Crossref","is-referenced-by-count":11,"title":["Numerical Discretization of a Darcy-Forchheimer Problem Coupled with a Singular Heat Equation"],"prefix":"10.1137","volume":"45","author":[{"given":"Alejandro","family":"Allendes","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Valpara\u00edso, Chile."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-6435-4313","authenticated-orcid":true,"given":"Gilberto","family":"Campa\u00f1a","sequence":"additional","affiliation":[{"name":"Departamento de Ciencias, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Valpara\u00edso, Chile."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Enrique","family":"Ot\u00e1rola","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Valpara\u00edso, Chile."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,10,25]]},"reference":[{"key":"ref1","series-title":"Pure and Appl. 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