Robust virtual element methods for 3D stress-assisted diffusion problems
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909474530263040 |
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| author | Rubiano, Andres E. |
| author_facet | Rubiano, Andres E. |
| contents | This paper presents an initial exploration of stress-assisted diffusion problems in three dimensions within the framework of the virtual element method (VEM). Hilbert spaces enriched with parameter-weighted norms, the extended Babuška-Brezzi-Braess theory for perturbed saddle-point problems, and Banach fixed-point theory play a crucial role in performing a robust analysis of the fully coupled non-linear system. The proposed virtual element formulations are provided with appropriate projection, interpolation, and stabilisation operators that ensures the well-posedness of the discrete problem. Numerical simulations are conducted to show the accuracy, performance, and applicability of the method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01851 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robust virtual element methods for 3D stress-assisted diffusion problems Rubiano, Andres E. Numerical Analysis 65N99, 65Y99 This paper presents an initial exploration of stress-assisted diffusion problems in three dimensions within the framework of the virtual element method (VEM). Hilbert spaces enriched with parameter-weighted norms, the extended Babuška-Brezzi-Braess theory for perturbed saddle-point problems, and Banach fixed-point theory play a crucial role in performing a robust analysis of the fully coupled non-linear system. The proposed virtual element formulations are provided with appropriate projection, interpolation, and stabilisation operators that ensures the well-posedness of the discrete problem. Numerical simulations are conducted to show the accuracy, performance, and applicability of the method. |
| title | Robust virtual element methods for 3D stress-assisted diffusion problems |
| topic | Numerical Analysis 65N99, 65Y99 |
| url | https://arxiv.org/abs/2502.01851 |