Let f : R to R be a continuous flux function and let u be a solution to the inviscid scalar conservation law
For each epsilon > 0, let u" be a solution to the associated viscous conservation law
We establish the following error estimate for the solutions of these systems:
for all t in (0, T), where TV(u_0) denotes the total variation of u_0 on R.
This estimate generalizes the known result for the case of Lipschitz flux functions. Our result is useful for the method of vanishing viscosity and for other numerical methods.