Statistical solutions of hyperbolic systems of conservation laws: Numerical approximation
Peer reviewed, Journal article
Accepted version
Åpne
Permanent lenke
https://hdl.handle.net/11250/2650879Utgivelsesdato
2020Metadata
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- Institutt for matematiske fag [2530]
- Publikasjoner fra CRIStin - NTNU [38688]
Originalversjon
10.1142/S0218202520500141Sammendrag
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.