an:02141312
Zbl 1112.65085
Karlsen, K. H.; Towers, J. D.
Convergence of the Lax-Friedrichs scheme and stability for conservation laws with a discontinuous space-time dependent flux
EN
Chin. Ann. Math., Ser. B 25, No. 3, 287-318 (2004).
00109723
2004
j
65M12 35L65
conservation laws; Lax-Friedrichs scheme; entropy condition; compensated compactness; nonconvex fluxes
The paper presents a convergence proof for the Lax-Friedrichs finite difference scheme in the context of non-convex genuinely nonlinear scalar conservation laws of the form
\[
u_t+ f(k(x, t),u)_x= 0,
\]
where the coefficient \(k(x, t)\) is allowed to be discontinuous along curves in the \((x, t)\) plane. It is shown that a convergent subsequence of approximations produced by the Lax-Friedrichs scheme converges to an entropy solution, implying that the entire computed sequence converges.
Andreas Meister (Kassel)