Fast Sweeping Methods for Hyperbolic Systems of Conservation Laws at   Steady State II
  The idea of using fast sweeping methods for solving stationary systems of conservation laws has previously been proposed for efficiently computing solutions with sharp shocks. We further develop these methods to allow for a more challenging class of problems including problems with sonic points, shocks originating in the interior of the domain, rarefaction waves, and two-dimensional systems. We show that fast sweeping methods can produce higher-order accuracy. Computational results validate the claims of accuracy, sharp shock curves, and optimal computational efficiency. 
Bjorn Engquist and Brittany D. Froese and Yen-Hsi Richard Tsai
math.NA