Hybrid weakly over-penalised symmetric interior penalty method on anisotropic meshes
<|reference_start|>Hybrid weakly over-penalised symmetric interior penalty method on anisotropic meshes: In this study, we investigate a hybrid-type anisotropic weakly over-penalised symmetric interior penalty method for the Poisson equation on convex domains. Compared with the well-known hybrid discontinuous Galerkin methods, our approach is simple and easy to implement. Our primary contributions are the proposal of a new scheme and the demonstration of a proof for the consistency term, which allows us to estimate the anisotropic consistency error. The key idea of the proof is to apply the relation between the Raviart--Thomas finite element space and a discontinuous space. In numerical experiments, we compare the calculation results for standard and anisotropic mesh partitions.<|reference_end|>
@article{ishizaka2024hybrid,
    title={Hybrid weakly over-penalised symmetric interior penalty method on
  anisotropic meshes},
    author={Hiroki Ishizaka},
    journal={arXiv preprint arXiv:2404.15288},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.15288},
    primaryClass={math.NA cs.NA}
}