Giesselmann, Jan ; Meyer, Fabian ; Rohde, Christian (2019)
Error control for statistical solutions.
doi: 10.48550/arXiv.1912.04323
Report, Bibliographie
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.
| Item Type: | Report |
|---|---|
| Erschienen: | 2019 |
| Creators: | Giesselmann, Jan ; Meyer, Fabian ; Rohde, Christian |
| Type of entry: | Bibliographie |
| Title: | Error control for statistical solutions |
| Language: | English |
| Date: | 9 December 2019 |
| Publisher: | arXiv |
| Series: | Numerical Analysis |
| Edition: | 1. Version |
| DOI: | 10.48550/arXiv.1912.04323 |
| URL / URN: | https://arxiv.org/abs/1912.04323 |
| 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. |
| Additional Information: | Preprint |
| Divisions: | 04 Department of Mathematics 04 Department of Mathematics > Numerical Analysis and Scientific Computing |
| Date Deposited: | 24 Apr 2020 08:45 |
| Last Modified: | 29 May 2024 10:28 |
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