Finite volume schemes for nonhomogeneous scalar conservation laws: error estimate

In this paper, we study nite 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 stii or nonstii. In both cases, we prove error estimates between the approximate solution given by a nite volume scheme (the scheme is totally explicit in the nonstii case, semi-implicit in the stii 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 stiiness of the source term in the stii case.