A Mixed finite element method for the velocity-pseudostress formulation of the Oseen eigenvalue problem
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914957322354688 |
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| author | Lepe, Felipe Rivera, Gonzalo Vellojin, Jesus |
| author_facet | Lepe, Felipe Rivera, Gonzalo Vellojin, Jesus |
| contents | In this paper, we introduce and analyze a mixed formulation for the Oseen eigenvalue problem by introducing the pseudostress tensor as a new unknown, allowing us to eliminate the fluid pressure. The well-posedness of the solution operator is established using a fixed-point argument. For the numerical analysis, we use the tensorial versions of Raviart-Thomas and Brezzi-Douglas-Marini elements to approximate the pseudostress, and piecewise polynomials for the velocity. Convergence and a priori error estimates are derived based on compact operator theory. We present a series of numerical tests in two and three dimensions to confirm the theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17314 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Mixed finite element method for the velocity-pseudostress formulation of the Oseen eigenvalue problem Lepe, Felipe Rivera, Gonzalo Vellojin, Jesus Numerical Analysis In this paper, we introduce and analyze a mixed formulation for the Oseen eigenvalue problem by introducing the pseudostress tensor as a new unknown, allowing us to eliminate the fluid pressure. The well-posedness of the solution operator is established using a fixed-point argument. For the numerical analysis, we use the tensorial versions of Raviart-Thomas and Brezzi-Douglas-Marini elements to approximate the pseudostress, and piecewise polynomials for the velocity. Convergence and a priori error estimates are derived based on compact operator theory. We present a series of numerical tests in two and three dimensions to confirm the theoretical findings. |
| title | A Mixed finite element method for the velocity-pseudostress formulation of the Oseen eigenvalue problem |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2409.17314 |