A geometric approach to error estimates for conservation laws posed on a spacetime

We consider a hyperbolic conservation law posed on an (N+1)(N+1)-dimensional spacetime, whose flux is a field of differential forms of degree NN. Generalizing the classical Kuznetsov’s method, we derive an L1L1 error estimate which applies to a large class of approximate solutions. In particular, we apply our main theorem and deal with two entropy solutions associated with distinct flux fields, as well as with an entropy solution and an approximate solution. Our framework encompasses, for instance, equations posed on a globally hyperbolic Lorentzian manifold.