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：在本文件中,我们研究了非线性部分差价方程式的克鲁塞克斯-拉维亚近似值,这些非线性部分差价方程式结构为$(p,\delta)$(1,\ infty)$和$\delta\ge 0$。我们确定了一个先验误差估计数,对所有美元(1,\ infty)$和$(delta\ge 0)美元最合适,美地乌斯误差估计数,即最佳准误差结果,以及初步的事后误差估计数,这些估计数既可靠又有效。理论结果得到了数字实验的支持。