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

Daniele Antonio Di Pietro (1) , Jérôme Droniou (2) , André Harnist (1)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 School of Mathematics [Australia]

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.

Mots clés: Hybrid High-Order methods; degenerate Leray-Lions problems; regime-dependent error estimates

Domaines: Analyse numérique [math.NA]

Daniele Antonio Di Pietro, Jérôme Droniou, André Harnist. Improved error estimates for Hybrid High-Order discretizations of Leray-Lions problems. 2020. ⟨hal-03049154v1⟩