Finite volume schemes for nonhomogeneous scalar conservation laws: error estimate

In this paper, we study finite volume schemes for the nonhomogeneous scalar conservation law u(t) + divF(x, t, u) = q(x, t, u) with initial condition u(x, 0) = u(0)(x). The source term may be either stiff or nonstiff. In both cases, we prove error estimates between the approximate solution given by a finite volume scheme (the scheme is totally explicit in the nonstiff case, semi-implicit in the stiff case) and the entropy solution. The order of these estimates is h(1)/(4) in space-time L-1-norm (h denotes the size of the mesh). Furthermore, the error estimate does not depend on the stiffness of the source term in the stiff case.