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arXiv · 2510.26375

Asymptotic meshes from $r$-variational adaptation methods for static problems in one dimension

Darith Hun·Nicolas Moës·Heiner Olbermann
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Abstract

We consider the minimization of integral functionals in one dimension and their approximation by $r$-adaptive finite elements. Including the grid of the FEM approximation as a variable in the minimization, we are able to show that the optimal grid configurations have a well-defined limit when the number of nodes in the grid is being sent to infinity. This is done by showing that the suitably renormalized energy functionals possess a limit in the sense of $\Gamma$-convergence. We provide numerical examples showing the closeness of the optimal asymptotic mesh obtained as a minimizer of the $\Gamma$-limit to the optimal finite meshes.

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Darith Hun, Nicolas Moës, Heiner Olbermann. 2025-10-30. Asymptotic meshes from $r$-variational adaptation methods for static problems in one dimension. https://arxiv.org/abs/2510.26375

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