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

2021/06/12 by Anna Kh. Balci, Christoph Ortner, Balci, Anna Kh. +3 · 1 citation
Computer Science · Engineering · Mathematics · #65M12 #65M60 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2106.06837

openalex publication_date 2021/06/12 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

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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