  Statistical solutions have recently been introduced as a an alternative
solution framework for hyperbolic systems of conservation laws. In this work we
derive a novel a posteriori error estimate in the Wasserstein distance between
dissipative statistical solutions and numerical approximations, which rely on
so-called regularized empirical measures. The error estimator can be split into
deterministic parts which correspond to spatio-temporal approximation errors
and a stochastic part which reflects the stochastic error. We provide numerical
experiments which examine the scaling properties of the residuals and verify
their splitting.

Numerical Analysis;Numerical Analysis