  Brenier and Grenier [SIAM J. Numer. Anal., 1998] proved that sticky particle
dynamics with a large number of particles allow to approximate the entropy
solution to scalar one-dimensional conservation laws with monotonic initial
data. In [arXiv:1501.01498], we introduced a multitype version of this dynamics
and proved that the associated empirical cumulative distribution functions
converge to the viscosity solution, in the sense of Bianchini and Bres-san
[Ann. of Math. (2), 2005], of one-dimensional diagonal hyperbolic systems with
monotonic initial data of arbitrary finite variation. In the present paper, we
analyse the L 1 error of this approximation procedure, by splitting it into the
discretisation error of the initial data and the non-entropicity error induced
by the evolution of the particle system. We prove that the error at time t is
bounded from above by a term of order (1 + t)/n, where n denotes the number of
particles, and give an example showing that this rate is optimal. We last
analyse the additional error introduced when replacing the multitype sticky
particle dynamics by an iterative scheme based on the typewise sticky particle
dynamics, and illustrate the convergence of this scheme by numerical
simulations.
