Sensitivity analysis of shallow water problems via perturbative methods

We applied the perturbative theory to perform sensitivity analysis of the shallow water equations. The numerical solution of these equations was found via the mass lumping finite element technique. Then, the adjoint system of the shallow water equations was derived for the one-dimensional case and the expression of the sensitivity coefficient of a generic functional with respect to a generic parameter (Chézy resistance coefficient, solitary wave amplitude and bed channel slope) was obtained, using the differential formalism. The sensitivity of the mean functional, representing the first appro...