Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

This article has been cited by the following article(s):

Spectral approximation of the Navier–Stokes equations coupled with the heat equation

J.M. Bernard
International Journal of Non-Linear Mechanics 44 (6) 581 (2009)
DOI: 10.1016/j.ijnonlinmec.2009.03.003
See this article

A Second Order Ensemble Timestepping Algorithm for Natural Convection

J. A. Fiordilino
SIAM Journal on Numerical Analysis 56 (2) 816 (2018)
DOI: 10.1137/17M1135104
See this article

Finite element methods for Darcy’s problem coupled with the heat equation

Christine Bernardi, Séréna Dib, Vivette Girault, Frédéric Hecht, François Murat and Toni Sayah
Numerische Mathematik 139 (2) 315 (2018)
DOI: 10.1007/s00211-017-0938-y
See this article

A Banach spaces-based analysis of a new fully-mixed finite element method for the Boussinesq problem

Eligio Colmenares, Gabriel N. Gatica and Sebastián Moraga
ESAIM: Mathematical Modelling and Numerical Analysis 54 (5) 1525 (2020)
DOI: 10.1051/m2an/2020007
See this article

Non-isothermal fluid flow through a thin pipe with cooling

Eduard Marušić-Paloka and Igor Pažanin
Applicable Analysis 88 (4) 495 (2009)
DOI: 10.1080/00036810902889542
See this article

New numerical studies for Darcy’s problem coupled with the heat equation

Dayana Dib, Séréna Dib and Toni Sayah
Computational and Applied Mathematics 39 (1) (2020)
DOI: 10.1007/s40314-019-0964-8
See this article

Natural convection in shallow water

Sanja Marušić
Nonlinear Analysis: Real World Applications 8 (5) 1379 (2007)
DOI: 10.1016/j.nonrwa.2005.10.009
See this article

Heat Conduction Problem in a Dilated Pipe: Existence and Uniqueness Result

Eduard Marušić-Paloka, Igor Pažanin and Marija Prša
Mediterranean Journal of Mathematics 14 (2) (2017)
DOI: 10.1007/s00009-017-0898-6
See this article

The steady Navier–Stokes/energy system with temperature-dependent viscosity—Part 1: Analysis of the continuous problem

Carlos E. Pérez, Jean-Marie Thomas, Serge Blancher and René Creff
International Journal for Numerical Methods in Fluids 56 (1) 63 (2008)
DOI: 10.1002/fld.1509
See this article

Rigorous derivation of the effective model describing a non-isothermal fluid flow in a vertical pipe filled with porous medium

Michal Beneš and Igor Pažanin
Continuum Mechanics and Thermodynamics 30 (2) 301 (2018)
DOI: 10.1007/s00161-017-0603-9
See this article

Effects of rough boundary on the heat transfer in a thin-film flow

Igor Pažanin and Francisco Javier Suárez-Grau
Comptes Rendus Mécanique 341 (8) 646 (2013)
DOI: 10.1016/j.crme.2013.05.001
See this article

Existence and uniqueness of the solution of a Boussinesq system with nonlinear dissipation

Dominique Blanchard, Nicolas Bruyère and Olivier Guibé
Communications on Pure and Applied Analysis 12 (5) 2213 (2013)
DOI: 10.3934/cpaa.2013.12.2213
See this article

Existence of a variational solution for the stationary Boussinesq equations with thermocapillary effect and nonhomogenous boundary conditions

Bernadin Ahounou and Luc Paquet
Afrika Matematika 27 (5-6) 909 (2016)
DOI: 10.1007/s13370-015-0386-8
See this article

A posteriori error analysis for solving the Navier-Stokes problem and convection-diffusion equation

Rahma Agroum
Numerical Methods for Partial Differential Equations 34 (2) 401 (2018)
DOI: 10.1002/num.22204
See this article

An Uzawa iterative method for the natural convection problem based on mixed finite element method

Xianzhu Li and Pengzhan Huang
Mathematical Methods in the Applied Sciences 44 (17) 13326 (2021)
DOI: 10.1002/mma.7627
See this article

The stationary Boussinesq problem under singular forcing

Alejandro Allendes, Enrique Otárola and Abner J. Salgado
Mathematical Models and Methods in Applied Sciences 31 (04) 789 (2021)
DOI: 10.1142/S0218202521500196
See this article

A mixed–primal finite element method for the Boussinesq problem with temperature-dependent viscosity

Javier A. Almonacid, Gabriel N. Gatica and Ricardo Oyarzúa
Calcolo 55 (3) (2018)
DOI: 10.1007/s10092-018-0278-z
See this article

An augmented fully-mixed finite element method for the stationary Boussinesq problem

Eligio Colmenares, Gabriel N. Gatica and Ricardo Oyarzúa
Calcolo 54 (1) 167 (2017)
DOI: 10.1007/s10092-016-0182-3
See this article

Spectral discretization of Darcy's equations coupled with the heat equation

Christine Bernardi, Sarra Maarouf and Driss Yakoubi
IMA Journal of Numerical Analysis 36 (3) 1193 (2016)
DOI: 10.1093/imanum/drv047
See this article

A Coupled Prediction Scheme for Solving the Navier--Stokes and Convection-Diffusion Equations

J. Deteix, A. Jendoubi and D. Yakoubi
SIAM Journal on Numerical Analysis 52 (5) 2415 (2014)
DOI: 10.1137/130942516
See this article

Modelling of heat transfer in a laminar flow through a helical pipe

Eduard Marušić-Paloka and Igor Pažanin
Mathematical and Computer Modelling 50 (11-12) 1571 (2009)
DOI: 10.1016/j.mcm.2009.09.006
See this article

A priori and a posteriori error estimations for the dual mixed finite element method of the Navier-Stokes problem

M. Farhloul, S. Nicaise and L. Paquet
Numerical Methods for Partial Differential Equations 25 (4) 843 (2009)
DOI: 10.1002/num.20377
See this article

A PROJECTION-BASED VARIATIONAL MULTISCALE METHOD FOR LARGE-EDDY SIMULATION WITH APPLICATION TO NON-ISOTHERMAL FREE CONVECTION PROBLEMS

JOHANNES LÖWE and GERT LUBE
Mathematical Models and Methods in Applied Sciences 22 (02) 1150011 (2012)
DOI: 10.1142/S0218202511500114
See this article

Full discretization of time dependent convection–diffusion–reaction equation coupled with the Darcy system

Nancy Chalhoub, Pascal Omnes, Toni Sayah and Rebecca El Zahlaniyeh
Calcolo 57 (1) (2020)
DOI: 10.1007/s10092-019-0352-1
See this article

Reduced Finite Element Discretizations of the Stokes and Navier-Stokes Equations

Petr Knobloch
Numerical Functional Analysis and Optimization 27 (2) 161 (2006)
DOI: 10.1080/01630560600569999
See this article

Numerical Solution of the Heat Transfer Equation Coupled with the Darcy Flow Using the Finite Element Method

Mohammed Hirpho and Chun Gang Zhu
Abstract and Applied Analysis 2022 1 (2022)
DOI: 10.1155/2022/5108445
See this article

On the coupling between a Navier–Stokes equation and a total energy equation in spatial dimension N=3

A. Attaoui
Journal of Differential Equations 246 (12) 4591 (2009)
DOI: 10.1016/j.jde.2008.12.003
See this article

A Divergence-Conforming DG-Mixed Finite Element Method for the Stationary Boussinesq Problem

Ricardo Oyarzúa and Miguel Serón
Journal of Scientific Computing 85 (1) (2020)
DOI: 10.1007/s10915-020-01317-7
See this article

Dual-mixed finite element methods for the stationary Boussinesq problem

Eligio Colmenares and Michael Neilan
Computers & Mathematics with Applications 72 (7) 1828 (2016)
DOI: 10.1016/j.camwa.2016.08.011
See this article

Impact of convection and radiation on direct/hybrid heating stability of field assisted sintering

Charles Manière, Flora Borie and Sylvain Marinel
Journal of Manufacturing Processes 56 147 (2020)
DOI: 10.1016/j.jmapro.2020.04.075
See this article

On the effects of curved geometry on heat conduction through a distorted pipe

Eduard Marušić-Paloka and Igor Pažanin
Nonlinear Analysis: Real World Applications 11 (6) 4554 (2010)
DOI: 10.1016/j.nonrwa.2008.09.016
See this article

Error estimates of finite element methods for nonstationary thermal convection problems with temperature-dependent coefficients

Masahisa Tabata and Daisuke Tagami
Numerische Mathematik 100 (2) 351 (2005)
DOI: 10.1007/s00211-005-0589-2
See this article

On the existence and uniqueness of the stationary solution to equations of natural convection with boundary data in L 2

M.Santos da Rocha, Marko A. Rojas-Medar and M. Drina Rojas-Medar
Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 459 (2031) 609 (2003)
DOI: 10.1098/rspa.2002.1036
See this article

Fixed point strategies for mixed variational formulations of the stationary Boussinesq problem

Eligio Colmenares, Gabriel N. Gatica and Ricardo Oyarzúa
Comptes Rendus Mathematique 354 (1) 57 (2016)
DOI: 10.1016/j.crma.2015.10.004
See this article

Analysis of a conforming finite element method for the Boussinesq problem with temperature-dependent parameters

Ricardo Oyarzúa and Paulo Zúñiga
Journal of Computational and Applied Mathematics 323 71 (2017)
DOI: 10.1016/j.cam.2017.04.009
See this article

M. El Hatri, R. Ghenji and N. Popivanov
2337 120005 (2021)
DOI: 10.1063/5.0041937
See this article

Lptheory for Boussinesq system with Dirichlet boundary conditions

Paul Acevedo, Chérif Amrouche and Carlos Conca
Applicable Analysis 98 (1-2) 272 (2019)
DOI: 10.1080/00036811.2018.1530762
See this article

Stabilized finite element approximations for a generalized Boussinesq problem: A posteriori error analysis

Alejandro Allendes, César Naranjo and Enrique Otárola
Computer Methods in Applied Mechanics and Engineering 361 112703 (2020)
DOI: 10.1016/j.cma.2019.112703
See this article

A posteriori error analysis of an augmented mixed-primal formulation for the stationary Boussinesq model

Eligio Colmenares, Gabriel N. Gatica and Ricardo Oyarzúa
Calcolo 54 (3) 1055 (2017)
DOI: 10.1007/s10092-017-0219-2
See this article

Boussinesq system with non-homogeneous boundary conditions

Paul Acevedo, Chérif Amrouche and Carlos Conca
Applied Mathematics Letters 53 39 (2016)
DOI: 10.1016/j.aml.2015.09.015
See this article

M. El Hatri, R. Ghenji and N. Popivanov
2172 030018 (2019)
DOI: 10.1063/1.5133507
See this article

The steady Navier–Stokes/energy system with temperature-dependent viscosity—Part 2: The discrete problem and numerical experiments

Carlos E. Pérez, Jean-Marie Thomas, Serge Blancher and René Creff
International Journal for Numerical Methods in Fluids 56 (1) 91 (2008)
DOI: 10.1002/fld.1572
See this article

A divergence-free low-order stabilized finite element method for a generalized steady state Boussinesq problem

Alejandro Allendes, Gabriel R. Barrenechea and César Naranjo
Computer Methods in Applied Mechanics and Engineering 340 90 (2018)
DOI: 10.1016/j.cma.2018.05.020
See this article

On the Darcy–Brinkman–Boussinesq Flow in a Thin Channel with Irregularities

Eduard Marušić-Paloka, Igor Pažanin and Marko Radulović
Transport in Porous Media 131 (2) 633 (2020)
DOI: 10.1007/s11242-019-01360-5
See this article

A new mixed-FEM for steady-state natural convection models allowing conservation of momentum and thermal energy

Sergio Caucao, Ricardo Oyarzúa and Segundo Villa-Fuentes
Calcolo 57 (4) (2020)
DOI: 10.1007/s10092-020-00385-3
See this article

An Lp spaces-based formulation yielding a new fully mixed finite element method for the coupled Darcy and heat equations

Gabriel N Gatica, Salim Meddahi and Ricardo Ruiz-Baier
IMA Journal of Numerical Analysis (2021)
DOI: 10.1093/imanum/drab063
See this article

Existence de solutions pour une classe de systèmes non linéaires de Boussinesq

Abdelatif Attaoui
Comptes Rendus Mathematique 346 (9-10) 515 (2008)
DOI: 10.1016/j.crma.2008.03.022
See this article

About one splitting scheme for the nonlinear problem of thermal convection

Perizat B. Beisebay, Alija B. Aruova, Erbulat Akzhigitov and Murat Sh. Tilepiev
International Journal of Heat and Mass Transfer 104 260 (2017)
DOI: 10.1016/j.ijheatmasstransfer.2016.08.050
See this article

Analysis of an augmented mixed-primal formulation for the stationary Boussinesq problem

Eligio Colmenares, Gabriel N. Gatica and Ricardo Oyarzúa
Numerical Methods for Partial Differential Equations 32 (2) 445 (2016)
DOI: 10.1002/num.22001
See this article

A mathematical model for thermography on viscous fluid based on damped thermal flux

Qasim Ali, Samia Riaz, Aziz Ullah Awan and Kashif Ali Abro
Zeitschrift für Naturforschung A 76 (3) 285 (2021)
DOI: 10.1515/zna-2020-0322
See this article

Regularity of the solutions of the steady-state Boussinesq equations with thermocapillarity effects on the surface of the liquid

Luc Paquet
Mathematical Methods in the Applied Sciences 22 (12) 1043 (1999)
DOI: 10.1002/(SICI)1099-1476(199908)22:12<1043::AID-MMA69>3.0.CO;2-3
See this article

An analysis of weak Galerkin finite element method for a steady state Boussinesq problem

Mehdi Dehghan and Zeinab Gharibi
Journal of Computational and Applied Mathematics 406 114029 (2022)
DOI: 10.1016/j.cam.2021.114029
See this article

Finite element methods for the Darcy-Forchheimer problem coupled with the convection-diffusion-reaction problem

Toni Sayah, Georges Semaan and Faouzi Triki
ESAIM: Mathematical Modelling and Numerical Analysis 55 (6) 2643 (2021)
DOI: 10.1051/m2an/2021066
See this article