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

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