NUMERICAL STABILITY AND ADAPTIVE METHODS FOR SOLVING THE SAINT-VENANT EQUATIONS

Solving the Saint-Venant (S-V) equations by FDM and FEM lead to some non-favorite oscillations for water surface elevation. In this paper, by using a suitable discretization, we solve the one dimensional SV equations by FEM and eliminate the non-favorite oscillations without using artificial viscosity. Then by using M-matrix properties we prove the stability of solution. Finally, we introduce three adaptive finite element methods which preserve the stability