Babuška's paradox in a nonlinear bending-folding model
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918225010229248 |
|---|---|
| author | Bartels, Sören Bonito, Andrea Hornung, Peter Neunteufel, Michael |
| author_facet | Bartels, Sören Bonito, Andrea Hornung, Peter Neunteufel, Michael |
| contents | The Babuška 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17190 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Babuška's paradox in a nonlinear bending-folding model Bartels, Sören Bonito, Andrea Hornung, Peter Neunteufel, Michael Numerical Analysis 74K20 74G65 65N30 The Babuška 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. |
| title | Babuška's paradox in a nonlinear bending-folding model |
| topic | Numerical Analysis 74K20 74G65 65N30 |
| url | https://arxiv.org/abs/2503.17190 |