AN ERROR ESTIMATE FOR THE APPROXIMATE SOLUTION OF A MULTIDIMENSIONAL CONSERVATION LAW EQUATION BY AN IMPLICIT FINITE-VOLUME SCHEME

In this Note we present an error estimate for the approximate solution of the nonlinear hyperbolic equation u(t) + div(f(u(x, t))v(x)) = 0 b y an implicit finite volume scheme. We show that the error is of order root k+root h, where h and k are respectively the sizes of the space and the time steps parameters. A generalisation of this result to an a rbitrary consistent monotone numerical flux is presented in [4]. The c onvergence of this scheme is possible with k/h (CFL condition) going t o infinity.