Conservation law with the flux function discontinuous in the space variable. II: Convex-concave type fluxes and generalized entropy solutions

DOI10.1016/j.cam.2006.04.009zbMath1131.65071OpenAlexW2059991999MaRDI QIDQ880180

Adimurthi, G. D. Veerappa Gowda, Siddhartha Mishra

Publication date: 11 May 2007

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2006.04.009

zbMATH Keywords

numerical experimentsconservation lawentropy solutionsnonlinear Cauchy problemtwo phase flowsGodunov finite difference methodoptimal entropy solutionsRankine-Hugoniot condition convergence

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Initial value problems for nonlinear first-order PDEs (35F25)

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Explicit Hopf-Lax type formulas for Hamilton-Jacobi equations and conservation laws with discontinuous coefficients ⋮ An Engquist-Osher type finite difference scheme with a discontinuous flux function in space ⋮ Multilevel Monte Carlo finite volume methods for random conservation laws with discontinuous flux ⋮ On the upstream mobility scheme for two-phase flow in porous media ⋮ Coupling techniques for nonlinear hyperbolic equations. II: Resonant interfaces with internal structure ⋮ Three models for two phase flow in porous media ⋮ Convergence Rates of Monotone Schemes for Conservation Laws with Discontinuous Flux ⋮ Convergence of Godunov type methods for a conservation law with a spatially varying discontinuous flux function ⋮ Shadow wave solutions for a scalar two-flux conservation law with Rankine–Hugoniot deficit

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