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

TL;DR

This paper presents new error estimates for Hybrid High-Order discretizations of Leray-Lions problems, showing how convergence rates depend on problem degeneracy and discretization degree, supported by numerical experiments.

Contribution

It introduces regime-dependent error estimates for HHO methods applied to Leray-Lions problems, advancing understanding of convergence behavior.

Findings

Convergence rate varies between (k+1)(p-1) and (k+1) depending on degeneracy.

Error estimates are validated through comprehensive numerical experiments.

The results improve theoretical understanding of HHO discretizations for nonlinear PDEs.

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.