Error analysis for a Crouzeix–Raviart approximation of the p-Dirichlet problem

Abstract

In the present paper, we examine a Crouzeix–Raviart approximation for non-linear partial differential equations having a (p, δ)-structure for some p ∈ (1, ∞) and δ⩾0. We establish a priori error estimates, which are optimal for all p ∈ (1, ∞) and δ⩾0, medius error estimates, i.e., best-approximation results, and a primal-dual a posteriori error estimate, which is both reliable and efficient. The theoretical findings are supported by numerical experiments.