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：我们针对具有有界初值的标量守恒律 $\partial_t u + \partial_x (H(x, u)) = 0$ 建立了一种有限体积格式，其中通量函数 $H$ 属于一大类关于第二个变量凸的函数。该格式构建的核心思想是利用间断通量理论。我们证明了由此生成的逼近序列在 $\mathopen]0, +\infty\mathclose[$ 上几乎处处有界收敛于熵解。