“…For simplicity only, we suppose from now on that B ≡ 1 in order to be able to use the explicit formulas (17). The next step is to study the properties of a relaxing scheme in the sense of [28,29] based on local Riemann problems of the type (12), (15), (18). More precisely, given any initial data (w 0 , z 0 ) in L 1 ∩ BV (R) and a space-step h > 0, we define the following sequences for j ∈ Z:…”