Giesselmann, Jan ; Meyer, Fabian ; Rohde, Christian (2019)
Error control for statistical solutions.
doi: 10.48550/arXiv.1912.04323
Report, Bibliographie
Kurzbeschreibung (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.
| Typ des Eintrags: | Report |
|---|---|
| Erschienen: | 2019 |
| Autor(en): | Giesselmann, Jan ; Meyer, Fabian ; Rohde, Christian |
| Art des Eintrags: | Bibliographie |
| Titel: | Error control for statistical solutions |
| Sprache: | Englisch |
| Publikationsjahr: | 9 Dezember 2019 |
| Verlag: | arXiv |
| Reihe: | Numerical Analysis |
| Auflage: | 1. Version |
| DOI: | 10.48550/arXiv.1912.04323 |
| URL / URN: | https://arxiv.org/abs/1912.04323 |
| Kurzbeschreibung (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. |
| Zusätzliche Informationen: | Preprint |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Numerik und wissenschaftliches Rechnen |
| Hinterlegungsdatum: | 24 Apr 2020 08:45 |
| Letzte Änderung: | 29 Mai 2024 10:28 |
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