I am looking for a site where i can find how to establish Shallow Watter Equations system and its resolution with finite element method

Hi there,

For the Shallow Water Equations you can look for example at the book of Pedlosky:

Pedlosky, 1987, Geophysical Fluid Dynamics, Springer Verlag, Berlin.

And for the Finite Element Method you can look at the book of Hughes:

Hugues, 1987, The Finite Element Methods (Prentice-Hall, New Jersey).

I am not really aware of any work solving the Shallow Water Equations with the Finite Element method, so I cannot give direct references on that. There is a tremendous amount of work done solving the time dependent 2D Shallow Water Equations using finite difference and especially using the spectral methods (for modeling planetary atmospheres, or for the weather prediction even; see e.g.

Cho and Polvani, 1996, Physics of Fluids, vol.8, page 1531.)

I hope this helps,

PG.