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We propose a spectral method based on the implementation of Chebyshevpolynomials to study a model of conservation laws on network. We avoid theGibbs phenomenon near shock discontinuities by implementing a filter in thefrequency space in order to add local viscosity able to contrast the spuriousoscillations appearing in the profile of the solution and we prove theconvergence of the semi-discrete method by using the compensated compactnesstheorem. thanks to several simulation, we make a comparison between theimplementation of the proposed method with a first order finite volume scheme.

A filtered Chebyshev spectral method for conservation laws on network