We consider a mono-dimensional two-velocities scheme used to approximate the solutions of a scalar hyperbolic conservative partial differential equation. We prove the convergence of the discrete solution toward the unique entropy solution by first estimating the supremum norm and the total variation of the discrete solution, and second by constructing a discrete kinetic entropy-entropy flux pair being given a continuous entropy-entropy flux pair of the hyperbolic system. We finally illustrate our results with numerical simulations of the advection equation and the Burgers equation.

翻译：我们考虑用于逼近标量双曲守恒型偏微分方程解的一维双速格式。通过先估计离散解的上确界范数和全变差，再基于双曲系统的连续熵-熵流对构造离散动力学熵-熵流对，证明了离散解向唯一熵解的收敛性。最后通过平流方程和Burgers方程的数值模拟验证了我们的结论。