Error control for statistical solutions of hyperbolic systems of conservation laws
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AbstractStatistical 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.
2004 ◽
Vol 35
(5)
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pp. 1347-1370
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2009 ◽
Vol 38
(9)
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pp. 1697-1709
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1968 ◽
Vol 74
(5)
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pp. 915-919
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2012 ◽
Vol 34
(4)
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pp. A2072-A2091
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