D. N. Arnold, J. Douglas, and V. Thomée, Superconvergence of a finite element approximation to the solution of a Sobolev equation in a single space variable, Mathematics of Computation, vol.36, issue.153, pp.53-64, 1981.
DOI : 10.1090/S0025-5718-1981-0595041-4

E. Audusse, A multilayer Saint-Venant System : Derivation and Numerical Validation, Discrete and Continuous Dynamical Systems, Ser. B, vol.5, issue.2, pp.189-214, 2005.

J. L. Bona, T. B. Benjamin, and J. J. Mahony, Model equations for long waves in nonlinear dispersive systems, Philos. Trans. Royal Soc. London Series A, vol.272, pp.47-78, 1972.

J. L. Bona, M. Chen, and J. C. Saut, Boussinesq Equations and Other Systems for Small-Amplitude Long Waves in Nonlinear Dispersive Media. I: Derivation and Linear Theory, Journal of Nonlinear Science, vol.12, issue.4, pp.283-318, 2002.
DOI : 10.1007/s00332-002-0466-4

F. Bouchut and M. Westdickenberg, Gravity driven shallow water models for arbitrary topography, Communications in Mathematical Sciences, vol.2, issue.3, pp.359-389, 2004.
DOI : 10.4310/CMS.2004.v2.n3.a2
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.138.8596

J. V. Boussinesq, Théorie de l'intumescence liquide appelée onde solitaire ou de translation se propageant dans un canal rectangulaire, C. R. Acad

R. Cienfuegos, E. Barthélemy, and P. Bonneton, A fourth-order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. Part I: model development and analysis, International Journal for Numerical Methods in Fluids, vol.37, issue.11, pp.1217-1253, 2006.
DOI : 10.1002/fld.1141
URL : https://hal.archives-ouvertes.fr/hal-00182841

S. Ferrari and F. Saleri, A new two-dimensional Shallow Water model including pressure effects and slow varying bottom topography, ESAIM: Mathematical Modelling and Numerical Analysis, vol.38, issue.2, pp.2-38, 2004.
DOI : 10.1051/m2an:2004010

J. Gerbeau and B. Perthame, Derivation of Viscous Saint-Venant System for Laminar Shallow Water; Numerical Validation, Discrete and Continuous Dynamical Systems, pp.89-102, 2001.

C. D. Levermore and M. Sammartino, A shallow water model with eddy viscosity for basins with varying bottom topography, Nonlinearity, vol.14, issue.6, pp.1493-1515, 2001.
DOI : 10.1088/0951-7715/14/6/305

P. L. Lions, Mathematical Topics in Fluid Mechanics, 1996.

F. Marche, Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects, European Journal of Mechanics - B/Fluids, vol.26, issue.1, pp.49-63, 2007.
DOI : 10.1016/j.euromechflu.2006.04.007

B. Mohammadi, O. Pironneau, and F. Valentin, Rough boundaries and wall laws, International Journal for Numerical Methods in Fluids, vol.318, issue.1-4, pp.169-177, 1998.
DOI : 10.1002/(SICI)1097-0363(199801)27:1/4<169::AID-FLD657>3.0.CO;2-4

O. Nwogu, Alternative Form of Boussinesq Equations for Nearshore Wave Propagation, Journal of Waterway, Port, Coastal, and Ocean Engineering, vol.119, issue.6, pp.618-638, 1993.
DOI : 10.1061/(ASCE)0733-950X(1993)119:6(618)

D. H. Peregrine, Long waves on a beach, Journal of Fluid Mechanics, vol.13, issue.04, pp.815-827, 1967.
DOI : 10.1017/S0022112067002605

S. Perotto and F. Saleri, Adaptive finite element methods for Boussinesq equations, Numerical Methods for Partial Differential Equations, vol.39, issue.2, pp.214-236, 2000.
DOI : 10.1002/(SICI)1098-2426(200003)16:2<214::AID-NUM5>3.0.CO;2-9

S. , S. Frazao, and Y. Zech, Undular bores and secondary waves -Experiments and hybrid finite-volume modelling, Journal of Hydraulic Research, vol.40, issue.1, pp.33-43, 2002.

M. A. Walkley, A numerical Method for Extended Boussinesq Shallow- Water Wave Equations, 1999.