Convergence of a Finite Volume Scheme for Compactly Heterogeneous Scalar Conservation Laws
<|reference_start|>Convergence of a Finite Volume Scheme for Compactly Heterogeneous Scalar Conservation Laws: 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.<|reference_end|>
@article{sylla2024convergence,
    title={Convergence of a Finite Volume Scheme for Compactly Heterogeneous Scalar
  Conservation Laws},
    author={Abraham Sylla},
    journal={arXiv preprint arXiv:2405.02203},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.02203},
    primaryClass={math.NA cs.NA}
}