Giesselmann, Jan ; Meyer, Fabian ; Rohde, Christian (2020)
A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws.
In: BIT Numerical Mathematics, 60
doi: 10.1007/s10543-019-00794-z
Article, Bibliographie
This is the latest version of this item.
Abstract
This article considers one-dimensional random systems of hyperbolic conservation laws. Existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws, which involve random initial data and random flux functions, are established. Based on these results an a posteriori error analysis for a numerical approximation of the random entropy solution is presented. For the stochastic discretization, a non-intrusive approach, namely the Stochastic Collocation method is used. The spatio-temporal discretization relies on the Runge–Kutta Discontinuous Galerkin method. The a posteriori estimator is derived using smooth reconstructions of the discrete solution. Combined with the relative entropy stability framework this yields computable error bounds for the entire space-stochastic discretization error. The estimator admits a splitting into a stochastic and a deterministic (space-time) part, allowing for a novel residual-based space-stochastic adaptive mesh refinement algorithm. The scaling properties of the residuals are investigated and the efficiency of the proposed adaptive algorithms is illustrated in various numerical examples.
| Item Type: | Article |
|---|---|
| Erschienen: | 2020 |
| Creators: | Giesselmann, Jan ; Meyer, Fabian ; Rohde, Christian |
| Type of entry: | Bibliographie |
| Title: | A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws |
| Language: | English |
| Date: | 2020 |
| Place of Publication: | Dordrecht [u.a.] |
| Publisher: | Springer Nature |
| Journal or Publication Title: | BIT Numerical Mathematics |
| Volume of the journal: | 60 |
| DOI: | 10.1007/s10543-019-00794-z |
| URL / URN: | https://link.springer.com/article/10.1007/s10543-019-00794-z |
| Corresponding Links: | |
| Abstract: | This article considers one-dimensional random systems of hyperbolic conservation laws. Existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws, which involve random initial data and random flux functions, are established. Based on these results an a posteriori error analysis for a numerical approximation of the random entropy solution is presented. For the stochastic discretization, a non-intrusive approach, namely the Stochastic Collocation method is used. The spatio-temporal discretization relies on the Runge–Kutta Discontinuous Galerkin method. The a posteriori estimator is derived using smooth reconstructions of the discrete solution. Combined with the relative entropy stability framework this yields computable error bounds for the entire space-stochastic discretization error. The estimator admits a splitting into a stochastic and a deterministic (space-time) part, allowing for a novel residual-based space-stochastic adaptive mesh refinement algorithm. The scaling properties of the residuals are investigated and the efficiency of the proposed adaptive algorithms is illustrated in various numerical examples. |
| Divisions: | 04 Department of Mathematics 04 Department of Mathematics > Numerical Analysis and Scientific Computing |
| Date Deposited: | 29 Apr 2020 08:35 |
| Last Modified: | 23 May 2024 08:21 |
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| Suche nach Titel in: | TUfind oder in Google |
Available Versions of this Item
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A posteriori error analysis based on non-intrusive spectral projections for systems of random conservation laws. (deposited 21 Oct 2019 09:38)
- A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws. (deposited 29 Apr 2020 08:35) [Currently Displayed]
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