Relative Entropy for the Numerical Diffusive Limit of the Linear Jin-Xin System
<|reference_start|>Relative Entropy for the Numerical Diffusive Limit of the Linear Jin-Xin System: This paper deals with the diffusive limit of the Jin and Xin model and its approximation by an asymptotic preserving finite volume scheme. At the continuous level, we determine a convergence rate to the diffusive limit by means of a relative entropy method. Considering a semi-discrete approximation (discrete in space and continuous in time), we adapt the method to this semi-discrete framework and establish that the approximated solutions converge towards the discrete convection-diffusion limit with the same convergence rate.<|reference_end|>
@article{bessemoulin-chatard2024relative,
    title={Relative Entropy for the Numerical Diffusive Limit of the Linear Jin-Xin
  System},
    author={Marianne Bessemoulin-Chatard (LMJL), H'el`ene Mathis (IMAG)},
    journal={arXiv preprint arXiv:2406.03268},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.03268},
    primaryClass={math.NA cs.NA}
}