Artificial diffusion mechanisms used to damp post-shock oscillations or to stabilize the computations contain a factor chi which determines the amount of diffusion provided. This paper suggests an improved procedure which consists of (1) varying chi from point to point depending on the local Courant number and (2) employing a value of local chi sub i which is determined from a monotonicity analysis. Results obtained by employing a locally dependent value of chi are compared with those for a global value of ch
