A Stokes-Brinkman-type formulation for the eigenvalue problem in porous media
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908445858332672 |
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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, for two and three dimensions, a finite element method to approximate the natural frequencies of a flow system governed by the Stokes-Brinkman equations. Here, the fluid presents the capability of being within a porous media. Taking advantage of the Stokes regularity results for the solution, and considering inf-sup stable families of finite elements, we prove convergence together with a priori and a posteriori error estimates for the eigenvalues and eigenfunctions with the aid of the compact operators theory. We report a series of numerical tests in order to confirm the developed theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_08226 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Stokes-Brinkman-type formulation for the eigenvalue problem in porous media Lepe, Felipe Rivera, Gonzalo Vellojin, Jesus Numerical Analysis 35Q35, 65N15, 65N25, 65N30, 65N50 In this paper we introduce and analyze, for two and three dimensions, a finite element method to approximate the natural frequencies of a flow system governed by the Stokes-Brinkman equations. Here, the fluid presents the capability of being within a porous media. Taking advantage of the Stokes regularity results for the solution, and considering inf-sup stable families of finite elements, we prove convergence together with a priori and a posteriori error estimates for the eigenvalues and eigenfunctions with the aid of the compact operators theory. We report a series of numerical tests in order to confirm the developed theory. |
| title | A Stokes-Brinkman-type formulation for the eigenvalue problem in porous media |
| topic | Numerical Analysis 35Q35, 65N15, 65N25, 65N30, 65N50 |
| url | https://arxiv.org/abs/2507.08226 |