The Neumann boundary condition for the two-dimensional Lax-Wendroff scheme II
<|reference_start|>The Neumann boundary condition for the two-dimensional Lax-Wendroff scheme II: We study the stability of a two-dimensional Lax-Wendroff scheme in a quarter-plane. Following our previous work, we aim here at adapting the energy method in order to study second order extrapolation boundary conditions. We first show on the one-dimensional problem why modifying the energy is a necessity in order to obtain stability estimates. We then study the two-dimensional case and propose a modified energy as well as second order extrapolation boundary and corner conditions in order to maintain second order accuracy and stability of the whole scheme, including near the corner.<|reference_end|>
@article{benoit2024the,
    title={The Neumann boundary condition for the two-dimensional Lax-Wendroff
  scheme. II},
    author={Antoine Benoit (LMPA), Jean-Franc{c}ois Coulombel (IMT)},
    journal={arXiv preprint arXiv:2405.19844},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.19844},
    primaryClass={math.NA cs.NA}
}