research
On interface transmission conditions for conservation laws with discontinuous flux of general shape
Abstract
International audienceConservation laws of the form with space-discontinuous flux were deeply investigated in the last ten years, with a particular emphasis in the case where the fluxes are ''bell-shaped". In this paper, we introduce and exploit the idea of transmission maps for the interface condition at the discontinuity, leading to the well-posedness for the Cauchy problem with general shape of . The design and the convergence of monotone Finite Volume schemes based on one-sided approximate Riemann solvers is then assessed. We conclude the paper by illustrating our approach by several examples coming from real-life applications- info:eu-repo/semantics/article
- Journal articles
- discontinuous flux
- hyperbolic conservation law
- monotone finite volume scheme
- interface coupling
- boundary layer
- convergent scheme
- well-posedness
- entropy solution
- interface flux
- 35L65, 35L04, 35D30, 65N08
- [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
- [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]