A noncoforming virtual element approximation for the Oseen eigenvalue problem
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916538407190528 |
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| author | Adak, Dibyendu Lepe, Felipe Rivera, Gonzalo |
| author_facet | Adak, Dibyendu Lepe, Felipe Rivera, Gonzalo |
| contents | In this paper we analyze a nonconforming virtual element method to approximate the eigenfunctions and eigenvalues of the two dimensional Oseen eigenvalue problem. The spaces under consideration lead to a divergence-free method which is capable to capture properly the divergence at discrete level and the eigenvalues and eigenfunctions. Under the compact theory for operators we prove convergence and error estimates for the method. By employing the theory of compact operators we recover the double order of convergence of the spectrum. Finally, we present numerical tests to assess the performance of the proposed numerical scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16813 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A noncoforming virtual element approximation for the Oseen eigenvalue problem Adak, Dibyendu Lepe, Felipe Rivera, Gonzalo Numerical Analysis In this paper we analyze a nonconforming virtual element method to approximate the eigenfunctions and eigenvalues of the two dimensional Oseen eigenvalue problem. The spaces under consideration lead to a divergence-free method which is capable to capture properly the divergence at discrete level and the eigenvalues and eigenfunctions. Under the compact theory for operators we prove convergence and error estimates for the method. By employing the theory of compact operators we recover the double order of convergence of the spectrum. Finally, we present numerical tests to assess the performance of the proposed numerical scheme. |
| title | A noncoforming virtual element approximation for the Oseen eigenvalue problem |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2412.16813 |