Statistical solutions have recently been introduced as 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 obtained from the Runge-Kutta Discontinuous Galerkin method in one spatial dimension, 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.

统计解决方案最近被引入，作为双曲守恒法律体系的替代解决方案框架。在这项工作中，我们推导了一种新颖的后验误差估计值，该值在耗散统计解与从一个空间维度上的Runge-Kutta间断Galerkin方法获得的数值近似值之间的Wasserstein距离中，后者依赖于所谓的正则化经验测度。误差估计器可以分为与时空近似误差相对应的确定性部分和反映随机误差的随机性部分。我们提供数值实验，检查残差的缩放属性并验证其分裂。