  We propose a spectral method based on the implementation of Chebyshev
polynomials to study a model of conservation laws on network. We avoid the
Gibbs phenomenon near shock discontinuities by implementing a filter in the
frequency space in order to add local viscosity able to contrast the spurious
oscillations appearing in the profile of the solution and we prove the
convergence of the semi-discrete method by using the compensated compactness
theorem. thanks to several simulation, we make a comparison between the
implementation of the proposed method with a first order finite volume scheme.
