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

In the present paper, we examine a Crouzeix–Raviart approximation of the p(· )-Dirichlet problem. We derive 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 Hölder continuous exponents and are optimal for Lipschitz continuous exponents. Numerical experiments are carried out to review the theoretical findings.