A filtered Chebyshev spectral method for conservation laws on network

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.