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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.

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