Statistical riemann problems and a composition law for errors in numerical solutions of shock physics problems

We seek error models for shock physics simulations that are robust and understandable. The purpose of this paper is to formulate and validate a composition law to estimate errors in the solutions of composite problems in terms of the errors from simpler ones. We illustrate this idea in a simple context. This paper employs several simplifying assumptions (restriction to one spatial dimension, use of a simplified (gamma law) equation of state, and consideration of a single numerical method). In separate papers we will address the effect of these assumptions.