Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap
Numerical Analysis
2021-06-15 v1 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2106.06837,
title = {Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap},
author = {Anna Kh. Balci and Christoph Ortner and Johannes Storn},
journal= {arXiv preprint arXiv:2106.06837},
year = {2021}
}