  We investigate the convergence of the Crouzeix-Raviart finite element method
for variational problems with non-autonomous integrands that exhibit
non-standard growth conditions. While conforming schemes fail due to the
Lavrentiev gap phenomenon, we prove that the solution of the Crouzeix-Raviart
scheme converges to a global minimiser. Numerical experiments illustrate the
performance of the scheme and give additional analytical insights.
