Error analysis for a Crouzeix-Raviart approximation of the variable exponent Dirichlet problem

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.