# An enhanced finite element method for a class of variational problems exhibiting the Lavrentiev gap phenomenon

10 Oct 2016 Feng Xiaobing Schnake Stefan

This paper develops an enhanced finite element method for approximating a class of variational problems which exhibit the \textit{Lavrentiev gap phenomenon} in the sense that the minimum values of the energy functional have a nontrivial gap when the functional is minimized on spaces $W^{1,1}$ and $W^{1,\infty}$. To remedy the standard finite element method, which fails to converge for such variational problems, a simple and effective cut-off procedure is utilized to design the (enhanced finite element) discrete energy functional... (read more)

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• NUMERICAL ANALYSIS