Improved error estimates for Hybrid High-Order discretizations of Leray-Lions problems

@article{Pietro2021ImprovedEE,
  title={Improved error estimates for Hybrid High-Order discretizations of Leray-Lions problems},
  author={Daniele A. Di Pietro and J{\'e}r{\^o}me Droniou and Andr'e Harnist},
  journal={ArXiv},
  year={2021},
  volume={abs/2012.05122}
}
We derive novel error estimates for Hybrid High-Order (HHO) discretizations of Leray-Lions problems set in W 1, p with p ∈ (1, 2]. Specifically, we prove that, depending on the degeneracy of the problem, the convergence rate may vary between (k + 1)(p − 1) and (k + 1), with k denoting the degree of the HHO approximation. These regime-dependent error estimates are illustrated by a complete panel of numerical experiments. 

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