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 W^(1,p) with p in (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.

20 pages, 4 figures, 4 tables

References in corpus (1)

• Unstabilized Hybrid High-Order method for a class of degenerate convex minimization problems

Cited by in corpus (3)

• An averaged space-time discretization of the stochastic $p$-Laplace system
• A Hybrid High-Order method for incompressible flows of non-Newtonian fluids with power-like convective behaviour
• A high-order local discontinuous Galerkin method for the $p$-Laplace equation