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

Abstract

We derive novel error estimates for Hybrid High-Order (HHO) discretizations of Leray–Lions problems set in W1,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.