  Fast sweeping methods have become a useful tool for computing the solutions
of static Hamilton-Jacobi equations. By adapting the main idea behind these
methods, we describe a new approach for computing steady state solutions to
systems of conservation laws. By exploiting the flow of information along
characteristics, these fast sweeping methods can compute solutions very
efficiently. Furthermore, the methods capture shocks sharply by directly
imposing the Rankine-Hugoniot shock conditions. We present convergence analysis
and numerics for several one- and two-dimensional examples to illustrate the
use and advantages of this approach.
