In the present paper, we examine a Crouzeix-Raviart approximation for non-linear partial differential equations having a $(p,\delta)$-structure for some $p\in (1,\infty)$ and $\delta\ge 0$. We establish a priori error estimates, which are optimal for all $p\in (1,\infty)$ and $\delta\ge 0$, 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.

翻译：本文研究了具有$(p,\delta)$-结构（其中$p\in(1,\infty)$，$\delta\ge 0$）的非线性偏微分方程的Crouzeix-Raviart逼近。我们建立了先验误差估计，该估计对任意$p\in(1,\infty)$和$\delta\ge 0$均为最优；同时给出了媒介误差估计（即最佳逼近结果）以及一种既可靠又高效的原-对偶后验误差估计。数值实验验证了理论结果的正确性。