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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.11603 |
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| _version_ | 1866909173476753408 |
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| author | Cangiani, Andrea Dedner, Andreas Hubbard, Matthew Wells, Harry |
| author_facet | Cangiani, Andrea Dedner, Andreas Hubbard, Matthew Wells, Harry |
| contents | We present two approaches to constructing isoparametric Virtual Element Methods of arbitrary order for linear elliptic partial differential equations on general two-dimensional domains. The first method approximates the variational problem transformed onto a computational reference domain. The second method computes a virtual domain and uses bespoke polynomial approximation operators to construct a computable method. Both methods are shown to converge optimally, a behaviour confirmed in practice for the solution of problems posed on curved domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11603 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Isoparametric Virtual Element Methods Cangiani, Andrea Dedner, Andreas Hubbard, Matthew Wells, Harry Numerical Analysis We present two approaches to constructing isoparametric Virtual Element Methods of arbitrary order for linear elliptic partial differential equations on general two-dimensional domains. The first method approximates the variational problem transformed onto a computational reference domain. The second method computes a virtual domain and uses bespoke polynomial approximation operators to construct a computable method. Both methods are shown to converge optimally, a behaviour confirmed in practice for the solution of problems posed on curved domains. |
| title | Isoparametric Virtual Element Methods |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2404.11603 |