A posteriori error estimates for a $C^1$ virtual element method applied to the thin plate vibration problem
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916834619424768 |
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| author | Dassi, Franco Rubiano, Andres E. Velásquez, Iván |
| author_facet | Dassi, Franco Rubiano, Andres E. Velásquez, Iván |
| contents | We propose and analyse residual-based a posteriori error estimates for the virtual element discretisation applied to the thin plate vibration problem in both two and three dimensions. Our approach involves a conforming $C^1$ discrete formulation suitable for meshes composed of polygons and polyhedra. The reliability and efficiency of the error estimator are established through a dimension-independent proof. Finally, several numerical experiments are reported to demonstrate the optimal performance of the method in 2D and 3D. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06846 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A posteriori error estimates for a $C^1$ virtual element method applied to the thin plate vibration problem Dassi, Franco Rubiano, Andres E. Velásquez, Iván Numerical Analysis We propose and analyse residual-based a posteriori error estimates for the virtual element discretisation applied to the thin plate vibration problem in both two and three dimensions. Our approach involves a conforming $C^1$ discrete formulation suitable for meshes composed of polygons and polyhedra. The reliability and efficiency of the error estimator are established through a dimension-independent proof. Finally, several numerical experiments are reported to demonstrate the optimal performance of the method in 2D and 3D. |
| title | A posteriori error estimates for a $C^1$ virtual element method applied to the thin plate vibration problem |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2507.06846 |