{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T00:55:04Z","timestamp":1773881704797,"version":"3.50.1"},"reference-count":59,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,11,16]],"date-time":"2024-11-16T00:00:00Z","timestamp":1731715200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,11,16]],"date-time":"2024-11-16T00:00:00Z","timestamp":1731715200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2025,1]]},"DOI":"10.1007\/s10915-024-02722-y","type":"journal-article","created":{"date-parts":[[2024,11,16]],"date-time":"2024-11-16T18:19:03Z","timestamp":1731781143000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Mixed Virtual Element Approximation for the Five-Field Formulation of the Steady Boussinesq Problem with Temperature-Dependent Parameters"],"prefix":"10.1007","volume":"102","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5462-0833","authenticated-orcid":false,"given":"Zeinab","family":"Gharibi","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,11,16]]},"reference":[{"issue":"6","key":"2722_CR1","doi-asserted-by":"crossref","first-page":"3396","DOI":"10.1093\/imanum\/drac072","volume":"43","author":"PF Antonietti","year":"2023","unstructured":"Antonietti, P.F., Vacca, G., Verani, M.: Virtual element method for the Navier\u2013Stokes equation coupled with the heat equation. IMA J. Numer. Anal. 43(6), 3396\u20133429 (2023)","journal-title":"IMA J. Numer. Anal."},{"key":"2722_CR2","doi-asserted-by":"crossref","first-page":"117079","DOI":"10.1016\/j.cma.2024.117079","volume":"428","author":"PF Antonietti","year":"2024","unstructured":"Antonietti, P.F., Beir\u00e3o da Veiga, L., Botti, M., Vacca, G., Verani, M.: A virtual element method for non-Newtonian pseudoplastic Stokes flows. Comput. Methods Appl. Mech. Eng. 428, 117079 (2024)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"3","key":"2722_CR3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10092-018-0278-z","volume":"55","author":"JA Almonacid","year":"2018","unstructured":"Almonacid, J.A., Gatica, G.N., Oyarz\u00faa, R.: A mixed-primal finite element method for the Boussinesq problem with temperature-dependent viscosity. Calcolo 55(3), 1\u201342 (2018)","journal-title":"Calcolo"},{"issue":"2","key":"2722_CR4","doi-asserted-by":"crossref","first-page":"215","DOI":"10.3934\/nhm.2020010","volume":"15","author":"JA Almonacid","year":"2020","unstructured":"Almonacid, J.A., Gatica, G.N., Oyarz\u00faa, R., Ruiz-Baier, R.: A new mixed finite element method for the n-dimensional Boussinesq problem with temperature-dependent viscosity. Netw. Heterog. Media 15(2), 215\u2013245 (2020)","journal-title":"Netw. Heterog. Media"},{"issue":"2","key":"2722_CR5","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1515\/cmam-2018-0187","volume":"20","author":"JA Almonacid","year":"2020","unstructured":"Almonacid, J.A., Gatica, G.N.: A fully-mixed finite element method for the n-dimensional Boussinesq problem with temperature-dependent parameters. Comput. Methods Appl. Math. 20(2), 187\u2013213 (2020)","journal-title":"Comput. Methods Appl. Math."},{"issue":"5","key":"2722_CR6","doi-asserted-by":"crossref","first-page":"1399","DOI":"10.1051\/m2an\/2015015","volume":"49","author":"M Alvarez","year":"2015","unstructured":"Alvarez, M., Gatica, G.N., Ruiz-Baier, R.: An augmented mixed-primal finite element method for a coupled flow-transport problem. ESAIM Math. Model. Numer. Anal. 49(5), 1399\u20131427 (2015)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"key":"2722_CR7","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1002\/fld.1650180705","volume":"18","author":"G Barakos","year":"1994","unstructured":"Barakos, G., Mitsoulis, E., Assimacopoulos, D.: Natural convection flow in a square cavity revisited: laminar and turbulent models with wall functions. Int. J. Numer. Methods Fluids. 18, 695\u2013719 (1994)","journal-title":"Int. J. Numer. Methods Fluids."},{"issue":"4","key":"2722_CR8","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.1051\/m2an\/2013138","volume":"48","author":"F Brezzi","year":"2014","unstructured":"Brezzi, F., Falk, R.S., Marini, L.D.: Basic principles of mixed virtual element methods. ESAIM Math. Model. Numer. Anal. 48(4), 1227\u20131240 (2014)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"key":"2722_CR9","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-3172-1","volume-title":"Mixed and Hybrid Finite Element Methods","author":"F Brezzi","year":"1991","unstructured":"Brezzi, F., Fortin, M.: Mixed and Hybrid Finite Element Methods. Springer, New York (1991)"},{"key":"2722_CR10","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1142\/S0218202512500492","volume":"23","author":"L Beir\u00e3o da Veiga","year":"2013","unstructured":"Beir\u00e3o da Veiga, L., Brezzi, F., Cangiani, A., Manzini, G., Marini, L.D., Russo, A.: Basic principles of virtual element methods. Math. Models Methods Appl. Sci. 23, 199\u2013214 (2013)","journal-title":"Math. Models Methods Appl. Sci."},{"issue":"2","key":"2722_CR11","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1051\/m2an\/2016032","volume":"51","author":"L Beir\u00e3o da Veiga","year":"2017","unstructured":"Beir\u00e3o da Veiga, L., Lovadina, C., Vacca, G.: Divergence free virtual elements for the Stokes problem on polygonal meshes. ESAIM Math. Model. Numer. Anal. 51(2), 509\u2013535 (2017)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"issue":"3","key":"2722_CR12","doi-asserted-by":"crossref","first-page":"1210","DOI":"10.1137\/17M1132811","volume":"56","author":"L Beir\u00e3o da Veiga","year":"2018","unstructured":"Beir\u00e3o da Veiga, L., Lovadina, C., Vacca, G.: Virtual elements for the Navier\u2013Stokes problem on polygonal meshes. SIAM J. Numer. Anal. 56(3), 1210\u20131242 (2018)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"2722_CR13","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1051\/m2an\/2015067","volume":"50","author":"L Beir\u00e3o da Veiga","year":"2016","unstructured":"Beir\u00e3o da Veiga, L., Brezzi, F., Marini, L.D., Russo, A.: Mixed virtual element methods for general second order elliptic problems on polygonal meshes. ESAIM Math. Model. Numer. Anal. 50(3), 727\u2013747 (2016)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"key":"2722_CR14","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2023.115947","volume":"408","author":"L Beir\u00e3o da Veiga","year":"2023","unstructured":"Beir\u00e3o da Veiga, L., Mora, D., Silgado, A.: A fully-discrete virtual element method for the nonstationary Boussinesq equations in stream-function form. Comput. Methods Appl. Mech. Eng. 408, 115947 (2023)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"2","key":"2722_CR15","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/s00211-015-0746-1","volume":"133","author":"L Beir\u00e3o da Veiga","year":"2016","unstructured":"Beir\u00e3o da Veiga, L., Brezzi, F., Marini, L.D., Russo, A.: $$H(\\rm div )$$ and $$H(\\textbf{curl} )$$-conforming virtual element methods. Numer. Math. 133(2), 303\u2013332 (2016)","journal-title":"Numer. Math."},{"issue":"2","key":"2722_CR16","doi-asserted-by":"crossref","first-page":"990","DOI":"10.1007\/s10915-019-01049-3","volume":"81","author":"L Beir\u00e3o da Veiga","year":"2019","unstructured":"Beir\u00e3o da Veiga, L., Mora, D., Vacca, G.: The Stokes complex for virtual elements with application to Navier\u2013Stokes flows. J. Sci. Comput. 81(2), 990\u20131018 (2019)","journal-title":"J. Sci. Comput."},{"issue":"7","key":"2722_CR17","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1051\/m2an\/1995290708711","volume":"29","author":"C Bernardi","year":"1995","unstructured":"Bernardi, C., M\u00e9tivet, B., Pernaud-Thomas, B.: Couplage des \u00e9quations de Navier-Stokes et de la chaleur: le mod\u00e9le et son approximation par \u00e9l\u00e9ments finis, (French) [Coupling of Navier-Stokes and heat equations: the model and its finite-element approximation]. RAIRO Mod\u00e9l. Math. Anal. Num\u00e9r. 29(7), 871\u2013921 (1995)","journal-title":"RAIRO Mod\u00e9l. Math. Anal. Num\u00e9r."},{"issue":"6","key":"2722_CR18","doi-asserted-by":"crossref","first-page":"1237","DOI":"10.1137\/0725070","volume":"25","author":"C Bernardi","year":"1988","unstructured":"Bernardi, C., Canuto, C., Maday, Y.: Generalized inf-sup conditions for Chebyshev spectral approximation of the Stokes problem. SIAM J. Numer. Anal. 25(6), 1237\u20131271 (1988)","journal-title":"SIAM J. Numer. Anal."},{"key":"2722_CR19","doi-asserted-by":"crossref","first-page":"114204","DOI":"10.1016\/j.cma.2021.114204","volume":"391","author":"MF Benedetto","year":"2022","unstructured":"Benedetto, M.F., Borio, A., Kyburg, F., Mollica, J., Scial\u00f2, S.: An arbitrary order mixed virtual element formulation for coupled multi-dimensional flow problems. Comput. Methods Appl. Mech. Eng. 391, 114204 (2022)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"1","key":"2722_CR20","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1016\/j.cam.2007.10.061","volume":"221","author":"L Boulaajine","year":"2008","unstructured":"Boulaajine, L., Nicaise, S., Paquet, L., Rafilipojaona: Dual mixed finite element methods for the elasticity problem with Lagrange multipliers. J. Comput. Appl. Math. 221(1), 234\u2013260 (2008)","journal-title":"J. Comput. Appl. Math."},{"issue":"1","key":"2722_CR21","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1093\/imanum\/drw002","volume":"37","author":"E C\u00e1ceres","year":"2017","unstructured":"C\u00e1ceres, E., Gatica, G.N.: A mixed virtual element method for the pseudostress-velocity formulation of the Stokes problem. IMA J. Numer. Anal. 37(1), 296\u2013331 (2017)","journal-title":"IMA J. Numer. Anal."},{"issue":"4","key":"2722_CR22","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1142\/S0218202517500142","volume":"27","author":"E C\u00e1ceres","year":"2017","unstructured":"C\u00e1ceres, E., Gatica, G.N., Sequeira, F.A.: A mixed virtual element method for the Brinkman problem. Math. Models Methods Appl. Sci. 27(4), 707\u2013743 (2017)","journal-title":"Math. Models Methods Appl. Sci."},{"key":"2722_CR23","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1137\/17M1121160","volume":"56","author":"E C\u00e1ceres","year":"2018","unstructured":"C\u00e1ceres, E., Gatica, G.N., Sequeira, F.A.: A mixed virtual element method for quasi-Newtonian Stokes flows. SIAM J. Numer. Anal. 56, 317\u2013343 (2018)","journal-title":"SIAM J. Numer. Anal."},{"key":"2722_CR24","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1002\/num.22001","volume":"32","author":"E Colmenares","year":"2016","unstructured":"Colmenares, E., Gatica, G.N., Oyarz\u00faa, R.: Analysis of an augmented mixed-primal formulation for the stationary Boussinesq problem. Numer. Methods Partial Differ. Equ. 32, 445\u2013478 (2016)","journal-title":"Numer. Methods Partial Differ. Equ."},{"issue":"5","key":"2722_CR25","doi-asserted-by":"crossref","first-page":"1525","DOI":"10.1051\/m2an\/2020007","volume":"54","author":"E Colmenares","year":"2020","unstructured":"Colmenares, E., Gatica, G.N., Moraga, S.: A Banach spaces-based analysis of a new fully-mixed finite element method for the Boussinesq problem. ESAIM Math. Model. Numer. Anal. 54(5), 1525\u20131568 (2020)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"key":"2722_CR26","doi-asserted-by":"crossref","unstructured":"Colmenares, E., Oyarz\u00faa, R., Pina, F.: Discontinuous Galerkin Method for the Stationary Boussinesq System. Comput. Methods Appl. Math. 22(4), 797\u2013820 (2022)","DOI":"10.1515\/cmam-2022-0021"},{"key":"2722_CR27","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/s10092-016-0182-3","volume":"54","author":"E Colmenares","year":"2017","unstructured":"Colmenares, E., Gatica, G.N., Oyarz\u00faa, R.: An augmented fully-mixed finite element method for the stationary Boussinesq problem. Calcolo 54, 167\u2013205 (2017)","journal-title":"Calcolo"},{"key":"2722_CR28","doi-asserted-by":"crossref","first-page":"2895","DOI":"10.1002\/num.22789","volume":"37","author":"J Cama\u00f1o","year":"2021","unstructured":"Cama\u00f1o, J., Garc\u00eda, C., Oyarz\u00faa, R.: Analysis of a momentum conservative mixed-FEM for the stationary Navier\u2013Stokes problem. Numer. Methods Partial Differ. Equ. 37, 2895\u20132923 (2021)","journal-title":"Numer. Methods Partial Differ. Equ."},{"key":"2722_CR29","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.camwa.2022.04.009","volume":"117","author":"CI Correa","year":"2022","unstructured":"Correa, C.I., Gatica, G.N.: On the continuous and discrete well-posedness of perturbed saddle-point formulations in Banach spaces. Comput. Math. Appl. 117, 14\u201323 (2022)","journal-title":"Comput. Math. Appl."},{"issue":"4","key":"2722_CR30","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1007\/s10092-020-00385-3","volume":"57","author":"S Caucao","year":"2020","unstructured":"Caucao, S., Oyarz\u00faa, R., Villa-Fuentes, S.: A new mixed-FEM for steady-state natural convection models allowing conservation of momentum and thermal energy. Calcolo 57(4), 36 (2020)","journal-title":"Calcolo"},{"key":"2722_CR31","volume-title":"The Finite Element Method for Elliptic Problems","author":"P Ciarlet","year":"1978","unstructured":"Ciarlet, P.: The Finite Element Method for Elliptic Problems. North-Holland (1978)"},{"issue":"1","key":"2722_CR32","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1007\/s10915-016-0191-z","volume":"69","author":"H Dallmann","year":"2016","unstructured":"Dallmann, H., Arndt, D.: Stabilized finite element methods for the Oberbeck\u2013Boussinesq model. J. Sci. Comput. 69(1), 244\u2013273 (2016)","journal-title":"J. Sci. Comput."},{"key":"2722_CR33","doi-asserted-by":"crossref","unstructured":"Demkowicz, L.F.: Mathematical Theory of Finite Elements, Society for Industrial and Applied Mathematics (2023)","DOI":"10.1137\/1.9781611977738"},{"issue":"3","key":"2722_CR34","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1080\/10407780500343749","volume":"49","author":"A Dalal","year":"2006","unstructured":"Dalal, A., Das, M.K.: Natural convection in a rectangular cavity heated from below and uniformly cooled from the top and both sides. Numer. Heat Transf. A Appl. 49(3), 301\u2013322 (2006)","journal-title":"Numer. Heat Transf. A Appl."},{"key":"2722_CR35","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1002\/fld.1650030305","volume":"3","author":"G De Vahl Davis","year":"1983","unstructured":"De Vahl Davis, G.: Natural convection of air in a square cavity: a bench mark numerical solution. Int. J. Numer. Methods Fluids 3, 249\u2013264 (1983)","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"2722_CR36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.camwa.2022.05.023","volume":"119","author":"F Dassi","year":"2022","unstructured":"Dassi, F., Fumagalli, A., Scotti, A., Vacca, G.: Bend 3D mixed virtual element method for Darcy problems. Comput. Math. Appl. 119, 1\u201312 (2022)","journal-title":"Comput. Math. Appl."},{"key":"2722_CR37","doi-asserted-by":"crossref","unstructured":"Dassi, F., Fumagalli, A., Mazzieri, I., Vacca, G.: Mixed Virtual Element approximation of linear acoustic wave equation. IMA J. Numer. Anal. (2023)","DOI":"10.1093\/imanum\/drad078"},{"key":"2722_CR38","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-4355-5","volume-title":"Theory and Practice of Finite Elements, Applied Mathematical Sciences","author":"A Ern","year":"2004","unstructured":"Ern, A., Guermond, J.-L.: Theory and Practice of Finite Elements, Applied Mathematical Sciences, vol. 159. Springer, New York (2004)"},{"issue":"14","key":"2722_CR39","doi-asserted-by":"crossref","first-page":"2937","DOI":"10.1142\/S0218202521500664","volume":"31","author":"GN Gatica","year":"2021","unstructured":"Gatica, G.N., Sequeira, F.A.: An $$L^p$$ spaces-based mixed virtual element method for the two-dimensional Navier\u2013Stokes equations. Math. Models Methods Appl. Sci. 31(14), 2937\u20132977 (2021)","journal-title":"Math. Models Methods Appl. Sci."},{"key":"2722_CR40","doi-asserted-by":"crossref","first-page":"2719","DOI":"10.1142\/S0218202518500598","volume":"28","author":"GN Gatica","year":"2018","unstructured":"Gatica, G.N., Munar, M., Sequeira, F.A.: A mixed virtual element method for the Navier\u2013Stokes equations. Math. Models Methods Appl. Sci. 28, 2719\u20132762 (2018)","journal-title":"Math. Models Methods Appl. Sci."},{"issue":"3","key":"2722_CR41","doi-asserted-by":"crossref","first-page":"392","DOI":"10.4208\/jcm.2001-m2019-0187","volume":"39","author":"GN Gatica","year":"2021","unstructured":"Gatica, G.N., Munar, M., Sequeira, F.A.: A mixed virtual element method for the Boussinesq problem on polygonal meshes. J. Comput. Math. 39(3), 392\u2013427 (2021)","journal-title":"J. Comput. Math."},{"issue":"2","key":"2722_CR42","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s10092-018-0262-7","volume":"55","author":"GN Gatica","year":"2018","unstructured":"Gatica, G.N., Munar, M., Sequeira, F.A.: A mixed virtual element method for a nonlinear Brinkman model of porous media flow. Calcolo 55(2), 21 (2018)","journal-title":"Calcolo"},{"key":"2722_CR43","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-03695-3","volume-title":"A Simple Introduction to the Mixed Finite Element Method. Theory and Applications. Springer-Briefs in Mathematics","author":"GN Gatica","year":"2014","unstructured":"Gatica, G.N.: A Simple Introduction to the Mixed Finite Element Method. Theory and Applications. Springer-Briefs in Mathematics. Springer, Cham (2014)"},{"key":"2722_CR44","unstructured":"Gatica, G.N.: Introducci\u00f3n al an\u00e1lisis funcional. Teor\u00eda y aplicaciones. Revert\u00e9 (2021)"},{"key":"2722_CR45","doi-asserted-by":"crossref","first-page":"115885","DOI":"10.1016\/j.cam.2024.115885","volume":"447","author":"GN Gatica","year":"2024","unstructured":"Gatica, G.N., Gharibi, Z.: A Banach spaces-based fully mixed virtual element method for the stationary two-dimensional Boussinesq equations. J. Comput. Appl. Math. 447, 115885 (2024)","journal-title":"J. Comput. Appl. Math."},{"key":"2722_CR46","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1016\/j.camwa.2021.01.001","volume":"84","author":"GN Gatica","year":"2021","unstructured":"Gatica, G.N., Oyarz\u00faa, R., Ruiz-Baier, R., Sobral, Y.D.: Banach spaces-based analysis of a fully-mixed finite element method for the steady-state model of fluidized beds. Comput. Math. Appl. 84, 244\u2013276 (2021)","journal-title":"Comput. Math. Appl."},{"issue":"5","key":"2722_CR47","doi-asserted-by":"crossref","first-page":"1312","DOI":"10.1016\/j.camwa.2018.11.008","volume":"77","author":"GN Gatica","year":"2019","unstructured":"Gatica, G.N., G\u00f3mez-Vargas, B., Ruiz-Baier, R.: formulation and analysis of fully-mixed methods for stress-assisted diffusion problems. Comput. Math. Appl. 77(5), 1312\u20131330 (2019)","journal-title":"Comput. Math. Appl."},{"key":"2722_CR48","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.apnum.2023.07.017","volume":"193","author":"GN Gatica","year":"2023","unstructured":"Gatica, G.N., Inzunza, C., Sequeira, F.A.: New Banach spaces-based fully-mixed finite element methods for pseudostress-assisted diffusion problems. Appl. Numer. Math. 193, 148\u2013178 (2023)","journal-title":"Appl. Numer. Math."},{"key":"2722_CR49","unstructured":"Grisvard, P.: Elliptic Problems in Nonsmooth Domains. Monographs Studies in Mathematics, 24 Pitman (Advanced Publishing Program), Boston (1985)"},{"key":"2722_CR50","unstructured":"Gharibi, Z., Dehghan, M.: A four-field Banach spaces-based mixed virtual element method for the unsteady two-dimensional Boussinesq equations with mixed boundary condition (2024) submitted"},{"key":"2722_CR51","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.camwa.2022.04.003","volume":"115","author":"Y Hou","year":"2022","unstructured":"Hou, Y., Yan, W., Li, M., He, X.: A decoupled and iterative finite element method for generalized Boussinesq equations. Comput. Math. Appl. 115, 14\u201325 (2022)","journal-title":"Comput. Math. Appl."},{"issue":"4","key":"2722_CR52","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1007\/s00211-011-0372-5","volume":"118","author":"JS Howell","year":"2011","unstructured":"Howell, J.S., Walkington, N.J.: Inf-sup conditions for twofold saddle point problems. Numer. Math. 118(4), 663\u2013693 (2011)","journal-title":"Numer. Math."},{"key":"2722_CR53","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.cam.2017.04.009","volume":"323","author":"R Oyarz\u00faa","year":"2017","unstructured":"Oyarz\u00faa, R., Z\u00fa\u00f1iga, P.: Analysis of a conforming finite element method for the Boussinesq problem with temperature-dependent parameters. J. Comput. Appl. Math. 323, 71\u201394 (2017)","journal-title":"J. Comput. Appl. Math."},{"issue":"3","key":"2722_CR54","doi-asserted-by":"crossref","first-page":"1104","DOI":"10.1093\/imanum\/drt043","volume":"34","author":"R Oyarz\u00faa","year":"2014","unstructured":"Oyarz\u00faa, R., Qin, T., Sch\u00f6tzau, D.: An exactly divergence-free finite element method for a generalized Boussinesq problem. IMA J. Numer. Anal. 34(3), 1104\u20131135 (2014)","journal-title":"IMA J. Numer. Anal."},{"key":"2722_CR55","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1007\/s10915-020-01317-7","volume":"85","author":"R Oyarz\u00faa","year":"2020","unstructured":"Oyarz\u00faa, R., Ser\u00f3n, M.: A divergence-conforming DG-mixed finite element method for the stationary Boussinesq problem. J. Sci. Comput. 85, 14 (2020)","journal-title":"J. Sci. Comput."},{"key":"2722_CR56","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1016\/j.jcp.2017.01.055","volume":"335","author":"PW Schroeder","year":"2017","unstructured":"Schroeder, P.W., Lube, G.: Stabilised dG-FEM for incompressible natural convection flows with boundary and moving interior layers on non-adapted meshes. J. Comput. Phys. 335, 760\u2013779 (2017)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"2722_CR57","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/s00211-005-0589-2","volume":"100","author":"M Tabata","year":"2005","unstructured":"Tabata, M., Tagami, D.: Error estimates of finite element methods for nonstationary thermal convection problems with temperature-dependent coefficients. Numer. Math. 100(2), 351\u2013372 (2005)","journal-title":"Numer. Math."},{"issue":"1","key":"2722_CR58","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1142\/S0218202518500057","volume":"28","author":"G Vacca","year":"2018","unstructured":"Vacca, G.: An $$H^1$$-conforming virtual element for Darcy and Brinkman equations. Math. Models Methods Appl. Sci. 28(1), 159\u2013194 (2018)","journal-title":"Math. Models Methods Appl. Sci."},{"key":"2722_CR59","doi-asserted-by":"crossref","first-page":"776","DOI":"10.1016\/j.jcp.2017.07.045","volume":"348","author":"J Wu","year":"2017","unstructured":"Wu, J., Shen, J., Feng, X.: Unconditionally stable gauge-Uzawa finite element schemes for incompressible natural convection problems with variable density. J. Comput. Phys. 348, 776\u2013789 (2017)","journal-title":"J. Comput. Phys."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-024-02722-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-024-02722-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-024-02722-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,13]],"date-time":"2025-01-13T15:00:51Z","timestamp":1736780451000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-024-02722-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,16]]},"references-count":59,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["2722"],"URL":"https:\/\/doi.org\/10.1007\/s10915-024-02722-y","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,11,16]]},"assertion":[{"value":"4 March 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 September 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 October 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 November 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"4"}}