Couplage des équations de Navier-Stokes et de la chaleur : le modèle et son approximation par éléments finis
ESAIM: M2AN, 29 7 (1995) 871-921
Published online: 2017-01-31
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):
Well -posedness of coupled Navier-Stokes and advection-diffusion equations for propagation of reaction fronts in viscous fluids
Mofdi El-Amrani, Anouar Obbadi, Mohammed Seaid and Driss YakoubiJournal of Computational and Applied Mathematics 481 117277 (2026)
https://doi.org/10.1016/j.cam.2025.117277
Finite Element Approximation for A Convective Brinkman–Forchheimer Problem Coupled with A Heat Equation
Gilberto Campaña, Pablo Muñoz and Enrique OtárolaJournal of Scientific Computing 104 (1) (2025)
https://doi.org/10.1007/s10915-025-02932-y
1 (2025)
https://doi.org/10.1016/B978-0-44-313317-6.00007-X
A conforming finite element method for a nonisothermal fluid-membrane interaction
Jessika Camaño, Ricardo Oyarzúa, Miguel Serón and Manuel SolanoMathematics of Computation 95 (357) 29 (2025)
https://doi.org/10.1090/mcom/4045
A fractional time-stepping method for unsteady thermal convection in non-Newtonian fluids
Mofdi El-Amrani, Anouar Obbadi, Mohammed Seaid and Driss YakoubiCommunications in Nonlinear Science and Numerical Simulation 140 108350 (2025)
https://doi.org/10.1016/j.cnsns.2024.108350
Modelling of the Forchheimer-Extended Darcy–Brinkman–Boussinesq Flow Through a Thin Channel
Marko Radulović, Karol Hajduk and Luka ToljTransport in Porous Media 152 (11) (2025)
https://doi.org/10.1007/s11242-025-02233-w
Mixed Virtual Element Approximation for the Five-Field Formulation of the Steady Boussinesq Problem with Temperature-Dependent Parameters
Zeinab GharibiJournal of Scientific Computing 102 (1) (2025)
https://doi.org/10.1007/s10915-024-02722-y
An exactly divergence-free hybridized discontinuous Galerkin method for the generalized Boussinesq equations with singular heat source
Haitao LengESAIM: Mathematical Modelling and Numerical Analysis 58 (4) 1347 (2024)
https://doi.org/10.1051/m2an/2024037
A finite element model for concentration polarization and osmotic effects in a membrane channel
Nicolás Carro, David Mora and Jesus VellojinInternational Journal for Numerical Methods in Fluids 96 (5) 601 (2024)
https://doi.org/10.1002/fld.5252
A time viscosity-splitting method for incompressible flows with temperature-dependent viscosity and thermal conductivity
Mofdi El-Amrani, Anouar Obbadi, Mohammed Seaid and Driss YakoubiComputer Methods in Applied Mechanics and Engineering 429 117103 (2024)
https://doi.org/10.1016/j.cma.2024.117103
On the thermal flow through a porous annular region
Eduard Marušić-Paloka and Igor PažaninJournal of Engineering Mathematics 147 (1) (2024)
https://doi.org/10.1007/s10665-024-10379-7
A coupled model of the fluid flow with nonlinear slip Tresca boundary condition
Dania Ati, Rahma Agroum and Jonas KokoComputers & Mathematics with Applications 153 130 (2024)
https://doi.org/10.1016/j.camwa.2023.11.007
A Priori Error Analysis and Finite Element Approximations for a Coupled Model Under Nonlinear Slip Boundary Conditions
Dania Ati, Rahma Agroum and Jonas KokoJournal of Mathematical Fluid Mechanics 26 (3) (2024)
https://doi.org/10.1007/s00021-024-00882-3
Darcy’s problem coupled with the heat equation under singular forcing: analysis and discretization
Alejandro Allendes, Gilberto Campaña, Francisco Fuica and Enrique OtárolaIMA Journal of Numerical Analysis 44 (6) 3683 (2024)
https://doi.org/10.1093/imanum/drad094
A Banach spaces-based fully mixed virtual element method for the stationary two-dimensional Boussinesq equations
Gabriel N. Gatica and Zeinab GharibiJournal of Computational and Applied Mathematics 447 115885 (2024)
https://doi.org/10.1016/j.cam.2024.115885
Augmented spectral formulation for the Stokes problem with variable viscosity and mixed boundary conditions
C. Bousbiat, Y. Daikh, S. Maarouf and D. YakoubiCalcolo 60 (3) (2023)
https://doi.org/10.1007/s10092-023-00530-8
Numerical Discretization of a Darcy-Forchheimer Problem Coupled with a Singular Heat Equation
Alejandro Allendes, Gilberto Campaña and Enrique OtárolaSIAM Journal on Scientific Computing 45 (5) A2755 (2023)
https://doi.org/10.1137/22M1536340
Existence and uniqueness for a convective phase change model with temperature–dependent viscosity
Y. Belhamadia, J. Deteix, B. Jaffal-Mourtada and D. YakoubiJournal of Mathematical Analysis and Applications 527 (2) 127559 (2023)
https://doi.org/10.1016/j.jmaa.2023.127559
An iterative scheme for solving a coupled Darcy–convection–diffusion model
Mofdi El-Amrani, Loubna Salhi, Mohammed Seaid and Driss YakoubiJournal of Mathematical Analysis and Applications 517 (2) 126603 (2023)
https://doi.org/10.1016/j.jmaa.2022.126603
A stabilized finite element method for the Stokes–Temperature coupled problem
Rodolfo Araya, Cristian Cárcamo and Abner H. PozaApplied Numerical Mathematics 187 24 (2023)
https://doi.org/10.1016/j.apnum.2023.02.002
A fully-discrete virtual element method for the nonstationary Boussinesq equations in stream-function form
L. Beirão da Veiga, D. Mora and A. SilgadoComputer Methods in Applied Mechanics and Engineering 408 115947 (2023)
https://doi.org/10.1016/j.cma.2023.115947
Versatile mixed methods for non-isothermal incompressible flows
Edward A. Miller, Xi Chen and David M. WilliamsComputers & Mathematics with Applications 125 150 (2022)
https://doi.org/10.1016/j.camwa.2022.08.044
An analysis of weak Galerkin finite element method for a steady state Boussinesq problem
Mehdi Dehghan and Zeinab GharibiJournal of Computational and Applied Mathematics 406 114029 (2022)
https://doi.org/10.1016/j.cam.2021.114029
A Discontinuous Galerkin Method for the Stationary Boussinesq System
Eligio Colmenares, Ricardo Oyarzúa and Francisco PiñaComputational Methods in Applied Mathematics 22 (4) 797 (2022)
https://doi.org/10.1515/cmam-2022-0021
Numerical Solution of the Heat Transfer Equation Coupled with the Darcy Flow Using the Finite Element Method
Mohammed Hirpho and Chun Gang ZhuAbstract and Applied Analysis 2022 1 (2022)
https://doi.org/10.1155/2022/5108445
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-BaierIMA Journal of Numerical Analysis 42 (4) 3154 (2022)
https://doi.org/10.1093/imanum/drab063
A mathematical model for thermography on viscous fluid based on damped thermal flux
Qasim Ali, Samia Riaz, Aziz Ullah Awan and Kashif Ali AbroZeitschrift für Naturforschung A 76 (3) 285 (2021)
https://doi.org/10.1515/zna-2020-0322
An Uzawa iterative method for the natural convection problem based on mixed finite element method
Xianzhu Li and Pengzhan HuangMathematical Methods in the Applied Sciences 44 (17) 13326 (2021)
https://doi.org/10.1002/mma.7627
The stationary Boussinesq problem under singular forcing
Alejandro Allendes, Enrique Otárola and Abner J. SalgadoMathematical Models and Methods in Applied Sciences 31 (04) 789 (2021)
https://doi.org/10.1142/S0218202521500196
Finite element methods for the Darcy-Forchheimer problem coupled with the convection-diffusion-reaction problem
Toni Sayah, Georges Semaan and Faouzi TrikiESAIM: Mathematical Modelling and Numerical Analysis 55 (6) 2643 (2021)
https://doi.org/10.1051/m2an/2021066
2337 120005 (2021)
https://doi.org/10.1063/5.0041937
A fully-mixed finite element method for the steady state Oberbeck–Boussinesq system
Eligio Colmenares, Gabriel N. Gatica, Sebastián Moraga and Ricardo Ruiz-BaierThe SMAI Journal of computational mathematics 6 125 (2020)
https://doi.org/10.5802/smai-jcm.64
A Divergence-Conforming DG-Mixed Finite Element Method for the Stationary Boussinesq Problem
Ricardo Oyarzúa and Miguel SerónJournal of Scientific Computing 85 (1) (2020)
https://doi.org/10.1007/s10915-020-01317-7
Impact of convection and radiation on direct/hybrid heating stability of field assisted sintering
Charles Manière, Flora Borie and Sylvain MarinelJournal of Manufacturing Processes 56 147 (2020)
https://doi.org/10.1016/j.jmapro.2020.04.075
New numerical studies for Darcy’s problem coupled with the heat equation
Dayana Dib, Séréna Dib and Toni SayahComputational and Applied Mathematics 39 (1) (2020)
https://doi.org/10.1007/s40314-019-0964-8
On the Darcy–Brinkman–Boussinesq Flow in a Thin Channel with Irregularities
Eduard Marušić-Paloka, Igor Pažanin and Marko RadulovićTransport in Porous Media 131 (2) 633 (2020)
https://doi.org/10.1007/s11242-019-01360-5
Full discretization of time dependent convection–diffusion–reaction equation coupled with the Darcy system
Nancy Chalhoub, Pascal Omnes, Toni Sayah and Rebecca El ZahlaniyehCalcolo 57 (1) (2020)
https://doi.org/10.1007/s10092-019-0352-1
A Banach spaces-based analysis of a new fully-mixed finite element method for the Boussinesq problem
Eligio Colmenares, Gabriel N. Gatica and Sebastián MoragaESAIM: Mathematical Modelling and Numerical Analysis 54 (5) 1525 (2020)
https://doi.org/10.1051/m2an/2020007
Stabilized finite element approximations for a generalized Boussinesq problem: A posteriori error analysis
Alejandro Allendes, César Naranjo and Enrique OtárolaComputer Methods in Applied Mechanics and Engineering 361 112703 (2020)
https://doi.org/10.1016/j.cma.2019.112703
A new mixed-FEM for steady-state natural convection models allowing conservation of momentum and thermal energy
Sergio Caucao, Ricardo Oyarzúa and Segundo Villa-FuentesCalcolo 57 (4) (2020)
https://doi.org/10.1007/s10092-020-00385-3
2172 030018 (2019)
https://doi.org/10.1063/1.5133507
Lptheory for Boussinesq system with Dirichlet boundary conditions
Paul Acevedo, Chérif Amrouche and Carlos ConcaApplicable Analysis 98 (1-2) 272 (2019)
https://doi.org/10.1080/00036811.2018.1530762
Rigorous derivation of the effective model describing a non-isothermal fluid flow in a vertical pipe filled with porous medium
Michal Beneš and Igor PažaninContinuum Mechanics and Thermodynamics 30 (2) 301 (2018)
https://doi.org/10.1007/s00161-017-0603-9
A mixed–primal finite element method for the Boussinesq problem with temperature-dependent viscosity
Javier A. Almonacid, Gabriel N. Gatica and Ricardo OyarzúaCalcolo 55 (3) (2018)
https://doi.org/10.1007/s10092-018-0278-z
Finite element methods for Darcy’s problem coupled with the heat equation
Christine Bernardi, Séréna Dib, Vivette Girault, et al.Numerische Mathematik 139 (2) 315 (2018)
https://doi.org/10.1007/s00211-017-0938-y
A posteriori error analysis for solving the Navier‐Stokes problem and convection‐diffusion equation
Rahma AgroumNumerical Methods for Partial Differential Equations 34 (2) 401 (2018)
https://doi.org/10.1002/num.22204
A Second Order Ensemble Timestepping Algorithm for Natural Convection
J. A. FiordilinoSIAM Journal on Numerical Analysis 56 (2) 816 (2018)
https://doi.org/10.1137/17M1135104
A divergence-free low-order stabilized finite element method for a generalized steady state Boussinesq problem
Alejandro Allendes, Gabriel R. Barrenechea and César NaranjoComputer Methods in Applied Mechanics and Engineering 340 90 (2018)
https://doi.org/10.1016/j.cma.2018.05.020
An augmented fully-mixed finite element method for the stationary Boussinesq problem
Eligio Colmenares, Gabriel N. Gatica and Ricardo OyarzúaCalcolo 54 (1) 167 (2017)
https://doi.org/10.1007/s10092-016-0182-3
About one splitting scheme for the nonlinear problem of thermal convection
Perizat B. Beisebay, Alija B. Aruova, Erbulat Akzhigitov and Murat Sh. TilepievInternational Journal of Heat and Mass Transfer 104 260 (2017)
https://doi.org/10.1016/j.ijheatmasstransfer.2016.08.050
Heat Conduction Problem in a Dilated Pipe: Existence and Uniqueness Result
Eduard Marušić-Paloka, Igor Pažanin and Marija PršaMediterranean Journal of Mathematics 14 (2) (2017)
https://doi.org/10.1007/s00009-017-0898-6
Analysis of a conforming finite element method for the Boussinesq problem with temperature-dependent parameters
Ricardo Oyarzúa and Paulo ZúñigaJournal of Computational and Applied Mathematics 323 71 (2017)
https://doi.org/10.1016/j.cam.2017.04.009
A posteriori error analysis of an augmented mixed-primal formulation for the stationary Boussinesq model
Eligio Colmenares, Gabriel N. Gatica and Ricardo OyarzúaCalcolo 54 (3) 1055 (2017)
https://doi.org/10.1007/s10092-017-0219-2
Analysis of an augmented mixed‐primal formulation for the stationary Boussinesq problem
Eligio Colmenares, Gabriel N. Gatica and Ricardo OyarzúaNumerical Methods for Partial Differential Equations 32 (2) 445 (2016)
https://doi.org/10.1002/num.22001
Spectral discretization of Darcy's equations coupled with the heat equation
Christine Bernardi, Sarra Maarouf and Driss YakoubiIMA Journal of Numerical Analysis 36 (3) 1193 (2016)
https://doi.org/10.1093/imanum/drv047
Existence of a variational solution for the stationary Boussinesq equations with thermocapillary effect and nonhomogenous boundary conditions
Bernadin Ahounou and Luc PaquetAfrika Matematika 27 (5-6) 909 (2016)
https://doi.org/10.1007/s13370-015-0386-8
Boussinesq system with non-homogeneous boundary conditions
Paul Acevedo, Chérif Amrouche and Carlos ConcaApplied Mathematics Letters 53 39 (2016)
https://doi.org/10.1016/j.aml.2015.09.015
Dual-mixed finite element methods for the stationary Boussinesq problem
Eligio Colmenares and Michael NeilanComputers & Mathematics with Applications 72 (7) 1828 (2016)
https://doi.org/10.1016/j.camwa.2016.08.011
Fixed point strategies for mixed variational formulations of the stationary Boussinesq problem
Eligio Colmenares, Gabriel N. Gatica and Ricardo OyarzúaComptes Rendus. Mathématique 354 (1) 57 (2015)
https://doi.org/10.1016/j.crma.2015.10.004
A Coupled Prediction Scheme for Solving the Navier--Stokes and Convection-Diffusion Equations
J. Deteix, A. Jendoubi and D. YakoubiSIAM Journal on Numerical Analysis 52 (5) 2415 (2014)
https://doi.org/10.1137/130942516
Effects of rough boundary on the heat transfer in a thin-film flow
Igor Pažanin and Francisco Javier Suárez-GrauComptes Rendus. Mécanique 341 (8) 646 (2013)
https://doi.org/10.1016/j.crme.2013.05.001
Existence and uniqueness of the solution of a Boussinesq system with nonlinear dissipation
Olivier Guibé, Nicolas Bruyère and Dominique BlanchardCommunications on Pure and Applied Analysis 12 (5) 2213 (2013)
https://doi.org/10.3934/cpaa.2013.12.2213
A PROJECTION-BASED VARIATIONAL MULTISCALE METHOD FOR LARGE-EDDY SIMULATION WITH APPLICATION TO NON-ISOTHERMAL FREE CONVECTION PROBLEMS
JOHANNES LÖWE and GERT LUBEMathematical Models and Methods in Applied Sciences 22 (02) (2012)
https://doi.org/10.1142/S0218202511500114
On the effects of curved geometry on heat conduction through a distorted pipe
Eduard Marušić-Paloka and Igor PažaninNonlinear Analysis: Real World Applications 11 (6) 4554 (2010)
https://doi.org/10.1016/j.nonrwa.2008.09.016
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. PaquetNumerical Methods for Partial Differential Equations 25 (4) 843 (2009)
https://doi.org/10.1002/num.20377
Modelling of heat transfer in a laminar flow through a helical pipe
Eduard Marušić-Paloka and Igor PažaninMathematical and Computer Modelling 50 (11-12) 1571 (2009)
https://doi.org/10.1016/j.mcm.2009.09.006
On the coupling between a Navier–Stokes equation and a total energy equation in spatial dimensionN=3
A. AttaouiJournal of Differential Equations 246 (12) 4591 (2009)
https://doi.org/10.1016/j.jde.2008.12.003
Spectral approximation of the Navier–Stokes equations coupled with the heat equation
J.M. BernardInternational Journal of Non-Linear Mechanics 44 (6) 581 (2009)
https://doi.org/10.1016/j.ijnonlinmec.2009.03.003
Non-isothermal fluid flow through a thin pipe with cooling
Eduard Marušić-Paloka and Igor PažaninApplicable Analysis 88 (4) 495 (2009)
https://doi.org/10.1080/00036810902889542
Existence de solutions pour une classe de systèmes non linéaires de Boussinesq
Abdelatif AttaouiComptes Rendus. Mathématique 346 (9-10) 515 (2008)
https://doi.org/10.1016/j.crma.2008.03.022
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 CreffInternational Journal for Numerical Methods in Fluids 56 (1) 91 (2008)
https://doi.org/10.1002/fld.1572
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 CreffInternational Journal for Numerical Methods in Fluids 56 (1) 63 (2008)
https://doi.org/10.1002/fld.1509
Natural convection in shallow water
Sanja MarušićNonlinear Analysis: Real World Applications 8 (5) 1379 (2007)
https://doi.org/10.1016/j.nonrwa.2005.10.009
Reduced Finite Element Discretizations of the Stokes and Navier-Stokes Equations
Petr KnoblochNumerical Functional Analysis and Optimization 27 (2) 161 (2006)
https://doi.org/10.1080/01630560600569999
Error estimates of finite element methods for nonstationary thermal convection problems with temperature-dependent coefficients
Masahisa Tabata and Daisuke TagamiNumerische Mathematik 100 (2) 351 (2005)
https://doi.org/10.1007/s00211-005-0589-2
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-MedarProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 459 (2031) 609 (2003)
https://doi.org/10.1098/rspa.2002.1036
A historical survey of some mathematical aspects of Newtonian fluid flows
RKh ZeytounianApplied Mechanics Reviews 54 (6) 525 (2001)
https://doi.org/10.1115/1.1416153
A mixed formulation of Boussinesq equations: Analysis of nonsingular solutions
M. Farhloul, S. Nicaise and L. PaquetMathematics of Computation 69 (231) 965 (2000)
https://doi.org/10.1090/S0025-5718-00-01186-8
Regularity of the solutions of the steady-state Boussinesq equations with thermocapillarity effects on the surface of the liquid
Luc PaquetMathematical Methods in the Applied Sciences 22 (12) 1043 (1999)
https://doi.org/10.1002/(SICI)1099-1476(199908)22:12<1043::AID-MMA69>3.0.CO;2-3