In this work we present a rather general approach to approximate the solutions of nonlocal conservation laws. Thereby, we approximate in a first step the nonlocal term with an appropriate quadrature rule applied to the spatial discretization. Then, we apply a numerical flux function on the reduced problem. We present explicit conditions which such a numerical flux function needs to fulfill. These conditions guarantee the convergence to the weak entropy solution of the considered model class. Numerical examples validate our theoretical findings and demonstrate that the approach can be applied to further nonlocal problems.

翻译：在本文中，我们提出了一种相当通用的方法来逼近非局部守恒律的解。首先，通过将合适的求积法则应用于空间离散化来逼近非局部项。随后，在简化问题上应用数值通量函数。我们给出了此类数值通量函数需要满足的显式条件，这些条件保证了收敛到所考虑模型类的弱熵解。数值算例验证了我们的理论结果，并表明该方法可适用于更广泛的非局部问题。