{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T13:51:59Z","timestamp":1762005119415,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2019,9,29]],"date-time":"2019-09-29T00:00:00Z","timestamp":1569715200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["PGC2018-096696-B-I00"],"award-info":[{"award-number":["PGC2018-096696-B-I00"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this work, we numerically study a thermo-mechanical problem arising in poro-viscoelasticity with the type III thermal law. The thermomechanical model leads to a linear system of three coupled hyperbolic partial differential equations, and its weak formulation as three coupled parabolic linear variational equations. Then, using the finite element method and the implicit Euler scheme, for the spatial approximation and the discretization of the time derivatives, respectively, a fully discrete algorithm is introduced. A priori error estimates are proved, and the linear convergence is obtained under some suitable regularity conditions. Finally, some numerical results, involving one- and two-dimensional examples, are described, showing the accuracy of the algorithm and the dependence of the solution with respect to some constitutive parameters.<\/jats:p>","DOI":"10.3390\/sym11101214","type":"journal-article","created":{"date-parts":[[2019,9,30]],"date-time":"2019-09-30T05:58:33Z","timestamp":1569823113000},"page":"1214","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Analysis of a Poro-Thermo-Viscoelastic Model of Type III"],"prefix":"10.3390","volume":"11","author":[{"given":"Noelia","family":"Bazarra","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada I, Universidade de Vigo, ETSI Telecomunicaci\u00f3n, Campus As Lagoas Marcosende s\/n, 36310 Vigo, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0391-7661","authenticated-orcid":false,"given":"Jos\u00e9 A.","family":"L\u00f3pez-Campos","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda Mec\u00e1nica, M\u00e1quinas y Motores T\u00e9rmicos y Flu\u00eddos, Escola de Enxe\u00f1ar\u00eda Industrial, Campus As Lagoas Marcosende s\/n, 36310 Vigo, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marcos","family":"L\u00f3pez","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda Mec\u00e1nica, M\u00e1quinas y Motores T\u00e9rmicos y Flu\u00eddos, Escola de Enxe\u00f1ar\u00eda Industrial, Campus As Lagoas Marcosende s\/n, 36310 Vigo, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8055-3689","authenticated-orcid":false,"given":"Abraham","family":"Segade","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda Mec\u00e1nica, M\u00e1quinas y Motores T\u00e9rmicos y Flu\u00eddos, Escola de Enxe\u00f1ar\u00eda Industrial, Campus As Lagoas Marcosende s\/n, 36310 Vigo, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8533-1858","authenticated-orcid":false,"given":"Jos\u00e9 R.","family":"Fern\u00e1ndez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada I, Universidade de Vigo, ETSI Telecomunicaci\u00f3n, Campus As Lagoas Marcosende s\/n, 36310 Vigo, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,9,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/BF00041230","article-title":"Linear elastic materials with voids","volume":"13","author":"Cowin","year":"1983","journal-title":"J. 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