In the present paper, we examine a Crouzeix-Raviart approximation of the $p(\cdot)$-Dirichlet problem. We derive a $\textit{medius}$ error estimate, $\textit{i.e.}$, a best-approximation result, which holds for uniformly continuous exponents and implies $\textit{a priori}$ error estimates, which apply for H\"older continuous exponents and are optimal for Lipschitz continuous exponents. Numerical experiments are carried out to review the theoretical findings.

翻译：本文研究了变指数Dirichlet问题的Crouzeix-Raviart逼近。我们推导出一个$\textit{medius}$误差估计，即一个最佳逼近结果，该结果对一致连续指数成立，并蕴含$\textit{先验}$误差估计。该先验估计适用于Hölder连续指数，且对于Lipschitz连续指数是最优的。通过数值实验验证了理论结果。