2000 character limit reached
Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap (2106.06837v1)
Published 12 Jun 2021 in math.NA and cs.NA
Abstract: 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.