Ies , for example I use the Galerkin method for solve a system of ordinary differential equations

You can use a good stiff ODE solver along with the Galerkin method for the spatial part of the problem, as long as the intersection of the Galerkin subspace $V_h$ and the closed convex set $K$ "fills up" $K$ as $h\to0$. You will need to solve one or more finite dimensional variational inequalities at each time step. There are a number of ways of doing this, ranging from using optimization algorithms to using non-smooth Newton methods. Because of the non-smoothness of the solution, high order methods are usually not recommended; implicit Euler in time, piecewise linear in space is usually enough.