Conforming/Non-conforming Virtual Elements and application to elasticity problems in curved three-dimensional domains
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913166855766016 |
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| author | da Veiga, L. Beirão Dassi, F. Russo, A. Trezzi, M. |
| author_facet | da Veiga, L. Beirão Dassi, F. Russo, A. Trezzi, M. |
| contents | The Virtual Element Method (VEM) is a well-established framework for solving partial differential equations on polygonal and polyhedral meshes. In this paper, we introduce a novel hybrid VEM that integrates both conforming and nonconforming virtual spaces. We apply this formulation to a three-dimensional linear elasticity problem, providing rigorous theoretical analysis to demonstrate optimal convergence rates. Furthermore, we explore the extension of this approach to domains with curved boundaries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28041 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Conforming/Non-conforming Virtual Elements and application to elasticity problems in curved three-dimensional domains da Veiga, L. Beirão Dassi, F. Russo, A. Trezzi, M. Numerical Analysis The Virtual Element Method (VEM) is a well-established framework for solving partial differential equations on polygonal and polyhedral meshes. In this paper, we introduce a novel hybrid VEM that integrates both conforming and nonconforming virtual spaces. We apply this formulation to a three-dimensional linear elasticity problem, providing rigorous theoretical analysis to demonstrate optimal convergence rates. Furthermore, we explore the extension of this approach to domains with curved boundaries. |
| title | Conforming/Non-conforming Virtual Elements and application to elasticity problems in curved three-dimensional domains |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2605.28041 |