A Virtual Element Method on polyhedra with curved faces
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911179527421952 |
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| author | Prada, Daniele Brezzi, Franco Marini, L. Donatella |
| author_facet | Prada, Daniele Brezzi, Franco Marini, L. Donatella |
| contents | In this paper we construct conforming Virtual Element approximations on domains with curved boundary and/or internal curved interfaces, both in two and three dimensions. Our approach allows to impose both Dirichlet and Neumann non-homogeneous boundary conditions, and provides, for degree of accuracy $k \geq 1$, optimal convergence rates. Whenever the exact solution is a polynomial of degree $k$, local spaces of degree $k$ ensure satisfaction of the patch test. The proposed method is theoretically analyzed in the two-dimensional case, whereas it is numerically validated both in two and three dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23005 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Virtual Element Method on polyhedra with curved faces Prada, Daniele Brezzi, Franco Marini, L. Donatella Numerical Analysis 65N30 In this paper we construct conforming Virtual Element approximations on domains with curved boundary and/or internal curved interfaces, both in two and three dimensions. Our approach allows to impose both Dirichlet and Neumann non-homogeneous boundary conditions, and provides, for degree of accuracy $k \geq 1$, optimal convergence rates. Whenever the exact solution is a polynomial of degree $k$, local spaces of degree $k$ ensure satisfaction of the patch test. The proposed method is theoretically analyzed in the two-dimensional case, whereas it is numerically validated both in two and three dimensions. |
| title | A Virtual Element Method on polyhedra with curved faces |
| topic | Numerical Analysis 65N30 |
| url | https://arxiv.org/abs/2509.23005 |