Babu\v{s}ka's paradox in a nonlinear bending-folding model
Numerical Analysis
2025-12-02 v2 Numerical Analysis
Abstract
The Babu\v{s}ka or plate paradox concerns the failure of convergence when a domain with curved boundary is approximated by polygonal domains in linear bending problems with simply supported boundary conditions. It can be explained via a boundary integral representation of the total Gaussian curvature that is part of the Kirchhoff--Love bending energy. It is shown that the paradox also occurs for a nonlinear bending-folding model which enforces vanishing Gaussian curvature. A simple remedy that is compatible with simplicial finite element methods to avoid incorrect convergence is devised.
Keywords
Cite
@article{arxiv.2503.17190,
title = {Babu\v{s}ka's paradox in a nonlinear bending-folding model},
author = {Sören Bartels and Andrea Bonito and Peter Hornung and Michael Neunteufel},
journal= {arXiv preprint arXiv:2503.17190},
year = {2025}
}