We build a finite volume scheme for the scalar conservation law $\partial_t u + \partial_x (H(x, u)) = 0$ with bounded initial condition for a wide class of flux function $H$, convex with respect to the second variable. The main idea for the construction of the scheme is to use the theory of discontinuous flux. We prove that the resulting approximating sequence converges boundedly almost everywhere on $\mathopen]0, +\infty\mathclose[$ to the entropy solution.

翻译：针对一大类关于第二个变量凸的流通量函数$H$，我们为具有有界初始条件的标量守恒律$\partial_t u + \partial_x (H(x, u)) = 0$构建了一个有限体积格式。该格式构造的核心思想是利用间断流通量理论。我们证明了所得近似序列在$\mathopen]0, +\infty\mathclose[$上几乎处处有界收敛于熵解。