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arXiv · 1912.04323

Error control for statistical solutions

Jan Giesselmann·Fabian Meyer·Christian Rohde
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Abstract

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.

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Jan Giesselmann, Fabian Meyer, Christian Rohde. 2019-12-09. Error control for statistical solutions. https://doi.org/10.1007/s10092-021-00417-6

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