A Posteriori Error Estimates for Numerical Solutions to Hyperbolic Conservation Laws

This paper is concerned with a posteriori error bounds for wide class of numerical schemes, $$n\times n$$ hyperbolic conservation laws in one space dimension. These estimates are achieved by “post-processing algorithm”, checking that the solution retains small total variation, and computing its oscillation on suitable subdomains. The results apply, particular, to solutions obtained Godunov or Lax–Friedrichs scheme, backward Euler approximations, method periodic smoothing. Some implementations presented.