A time-fractional step method for conservation law related obstacle problems (Q1604347)

This paper deals with a general scalar conservation law associated with a forced unilateral constraint. To this end, the authors introduce the quasilinear first-order operator \[ u\mapsto \partial_t u+ \sum^p_{i=1} \partial_{x_i} f(u)-g(u), \] where only the dependence on \(u\) is taken into consideration in the transport and reaction terms. The author use the time-splitting method developed classically to compute discontinuous solutions of nonhomogeneous scalar conservation laws. The main goal of this paper is to estimate the \(L^1\)-error bound between the corresponding exact solution and the split one.