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arXiv · 2106.06837

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

Anna Kh. Balci·Christoph Ortner·Johannes Storn
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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.

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Anna Kh. Balci, Christoph Ortner, Johannes Storn. 2021-06-12. Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap. https://arxiv.org/abs/2106.06837

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