M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, American Journal of Physics, vol.34, issue.2, 1965.
DOI : 10.1119/1.1972842

A. Bejan, Convection heat transfer, 1995.
DOI : 10.1002/9781118671627

M. K. Choudhary, A Three-Dimensional Mathematical Model for Flow and Heat Transfer in Electrical Glass Furnaces, IEEE Transactions on Industry Applications, vol.22, issue.5, pp.22912-921, 1986.
DOI : 10.1109/TIA.1986.4504814

B. Cockburn, G. Kanschat, D. Schötzau, and C. Schwab, Local Discontinuous Galerkin Methods for the Stokes System, SIAM Journal on Numerical Analysis, vol.40, issue.1, pp.319-342, 2002.
DOI : 10.1137/S0036142900380121
URL : http://www.ima.umn.edu/preprints/oct2000/1728.ps

D. A. Di-pietro and A. Ern, Mathematical aspects of discontinuous Galerkin methods
DOI : 10.1007/978-3-642-22980-0

A. Ern and J. Guermond, Eléments finis : Théorie, applications, mise en oeuvre, 2002.

J. Flesselles and F. Pigeonneau, Kinematic regimes of convection at high Prandtl number in a shallow cavity, Comptes Rendus M??canique, vol.332, issue.10, pp.783-788, 2004.
DOI : 10.1016/j.crme.2004.06.003
URL : https://hal.archives-ouvertes.fr/hal-01442932

S. Gopalakrishnan, A. Thess, G. Weidmann, and U. Lange, Chaotic mixing in a Joule-heated glass melt, Physics of Fluids, vol.22, issue.1, p.13101, 2010.
DOI : 10.1088/1367-2630/11/7/075031

D. D. Joseph, Stability of fluid motions II, 1976.
DOI : 10.1007/978-3-642-80994-1

R. Krishnamurti, Some further studies on the transition to turbulent convection, Journal of Fluid Mechanics, vol.44, issue.02, pp.285-303, 1973.
DOI : 10.1063/1.1762379

F. A. Kulacki and R. J. Goldstein, Hydrodynamic instability in fluid layers with uniform volumetric energy sources, Applied Scientific Research, vol.55, issue.2, pp.81-109, 1975.
DOI : 10.1098/rspa.1940.0092

P. Manneville, Instabilities, Chaos and Turbulence, 2004.
DOI : 10.1142/p349

F. Pigeonneau, A. Cornet, and F. Lopépé, Thermoconvective instabilities of a non uniform Jouleheated liquid enclosed in a rectangular cavity, J. Fluid Mech, 2017.

F. Pigeonneau and J. Flesselles, Practical laws for natural convection of viscous fluids heated from above in a shallow cavity, International Journal of Heat and Mass Transfer, vol.55, issue.1-3, pp.436-442, 2012.
DOI : 10.1016/j.ijheatmasstransfer.2011.09.042
URL : https://hal.archives-ouvertes.fr/hal-00648070

P. H. Roberts, Convection in horizontal layers with internal heat generation. Theory, Journal of Fluid Mechanics, vol.31, issue.01, pp.33-49, 1967.
DOI : 10.1175/1520-0469(1963)020 2.0.CO;2

C. P. Ross and G. L. Tincher, Glass Melting Technology: A Technical and Economic Assessment, 2004.

P. Saramito, Efficient C++ finite element computing with Rheolef, 2015.
URL : https://hal.archives-ouvertes.fr/cel-00573970

P. Saramito, Efficient C++ finite element computing with Rheolef, Discontinuous Galerkin methods. CNRS-CCSD ed, 2015.
URL : https://hal.archives-ouvertes.fr/cel-00573970

H. Scholze, Glass. Nature, Structures and Properties, 1990.

J. Stanek, Electric melting of glass, Journal of Non-Crystalline Solids, vol.84, issue.1-3, 1977.
DOI : 10.1016/0022-3093(86)90797-0

G. Sugilal, P. K. Wattal, and K. Iyer, Convective behaviour of a uniformly Joule-heated liquid pool in a rectangular cavity, International Journal of Thermal Sciences, vol.44, issue.10, pp.915-925, 2005.
DOI : 10.1016/j.ijthermalsci.2005.03.012

E. Süli and D. F. Mayers, An Introduction to Numerical Analysis, 2003.
DOI : 10.1017/CBO9780511801181

R. Thirlby, Convection in an internally heated layer, Journal of Fluid Mechanics, vol.4, issue.04, pp.673-693, 1970.
DOI : 10.1063/1.1761178

K. E. Uguz, G. Labrosse, R. Narayanan, and F. Pigeonneau, From steady to unsteady horizontal gradient-driven convection at high Prandtl number, International Journal of Heat and Mass Transfer, vol.71, pp.469-474, 2014.
DOI : 10.1016/j.ijheatmasstransfer.2013.12.002
URL : https://hal.archives-ouvertes.fr/hal-00944745

R. Viskanta and E. E. Anderson, Heat transfer in semitransparent solids Advances in heat transfer, pp.317-441, 1975.