Name
Title | ||
|---|---|---|
Statistical solutions of hyperbolic systems of conservation laws: numerical approximation. |
Abstract | ||
|---|---|---|
Statistical solutions are time-parameterized probability measures on spaces of integrable functions, which have been proposed recently as a framework for global solutions and uncertainty quantification for multi-dimensional hyperbolic system of conservation laws. By combining high-resolution finite volume methods with a Monte Carlo sampling procedure, we present a numerical algorithm to approximate statistical solutions. Under verifiable assumptions on the finite volume method, we prove that the approximations, generated by the proposed algorithm, converge in an appropriate topology to a statistical solution. Numerical experiments illustrating the convergence theory and revealing interesting properties of statistical solutions are also presented. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1142/S0218202520500141 | MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES |
Keywords | DocType | Volume |
Hyperbolic systems,statistical solutions,probability measures,Wasserstein metric | Journal | 30 |
Issue | ISSN | Citations |
3 | 0218-2025 | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ulrik S. Fjordholm | 1 | 73 | 9.95 |
| Kjetil O. Lye | 2 | 2 | 0.80 |
| Siddhartha Mishra | 3 | 170 | 21.36 |
| Franziska Weber | 4 | 0 | 0.34 |