Convergence rate of the spectral difference method on regular triangular meshes
<|reference_start|>Convergence rate of the spectral difference method on regular triangular meshes: We consider the spectral difference method based on the p-th order Raviart~-- Thomas space (p=1,2,3) on regular triangular meshes for the scalar transport equation. The solution converges with the order p if the transport velocity is parallel to a family of mesh edges and with the order p+1 otherwise. We prove this fact for p=1 and show it for p=1,2,3 in numerical experiments.<|reference_end|>
@article{bakhvalov2024convergence,
    title={Convergence rate of the spectral difference method on regular triangular
  meshes},
    author={Pavel Bakhvalov},
    journal={arXiv preprint arXiv:2404.10391},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.10391},
    primaryClass={math.NA cs.NA}
}