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

Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap