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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1901.02228 |
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| _version_ | 1866912161460125696 |
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| author | Scholtes, Sebastian Schumacher, Henrik Wardetzky, Max |
| author_facet | Scholtes, Sebastian Schumacher, Henrik Wardetzky, Max |
| contents | We discuss a discretization by polygonal lines of the Euler-Bernoulli bending energy and of Euler elasticae under clamped boundary conditions. We show Hausdorff convergence of the set of almost minimizers of the discrete bending energy to the set of smooth Euler elasticae under mesh refinement in (i) the $W^{1,\infty}$-topology for piecewise-linear interpolation and in (ii) the $W^{2,p}$-topology, $p \in{[2,\infty[}$, using a suitable smoothing operator to create $W^{2,p}$-curves from polygons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_02228 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Variational Convergence of Discrete Elasticae Scholtes, Sebastian Schumacher, Henrik Wardetzky, Max Numerical Analysis 49Q10, 53A04 We discuss a discretization by polygonal lines of the Euler-Bernoulli bending energy and of Euler elasticae under clamped boundary conditions. We show Hausdorff convergence of the set of almost minimizers of the discrete bending energy to the set of smooth Euler elasticae under mesh refinement in (i) the $W^{1,\infty}$-topology for piecewise-linear interpolation and in (ii) the $W^{2,p}$-topology, $p \in{[2,\infty[}$, using a suitable smoothing operator to create $W^{2,p}$-curves from polygons. |
| title | Variational Convergence of Discrete Elasticae |
| topic | Numerical Analysis 49Q10, 53A04 |
| url | https://arxiv.org/abs/1901.02228 |