Convergence of a Godunov scheme for degenerate conservation laws with BV spatial flux and a study of Panov-type fluxes

We prove the convergence of Godunov-type scheme for a scalar conservation law in one space dimension with possibly infinitely many spatial discontinuities, which may have accumulation points. In contrast to study appearing Ghoshal, Jana and Towers [Convergence Godunov an Audusse–Perthame adapted entropy solution laws BV flux, Numer. Math. 146(3) (2020) 629–659], we do not restrict flux be unimodal allow case where has degeneracies due corresponding singular map invertible hence, so-called mapping technique is applicable. present two proofs depending on nature flux. For fluxes are piecewise constant variable, established by proving [Formula: see text] bounds finite volume approximations away from set discontinuity. On other hand, if Panov-type, i.e. text], establishing novel property, turn implies existence solution. numerical examples that illustrate theory.