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.

翻译：我们提出了一种基于切比雪夫多项式实现的谱方法，用于研究网络上的守恒律模型。通过在频率空间中引入滤波器以增加局部黏性，从而抑制解剖面中出现的虚假振荡，我们避免了激波间断附近的吉布斯现象，并利用补偿紧致定理证明了半离散方法的收敛性。通过多次数值模拟，我们将所提方法的结果与一阶有限体积格式进行了比较。