In the present paper, we examine a Crouzeix-Raviart approximation for non-linear partial differential equations having a $(p(\cdot),\delta)$-structure. We establish a medius error estimate, i.e., a best-approximation result, which holds for uniformly continuous exponents and implies a priori error estimates, which apply for H\"older continuous exponents and are optimal for Lipschitz continuous exponents. The theoretical findings are supported by numerical experiments.

翻译：本文研究了一类具有$(p(\cdot),\delta)$结构的非线性偏微分方程的Crouzeix-Raviart逼近。我们建立了一个中等误差估计，即一个最佳逼近结果，该结果适用于一致连续指数，并推导出先验误差估计，这些估计适用于Hölder连续指数，且对Lipschitz连续指数是最优的。理论发现得到了数值实验的支持。