Discontinuous Galerkin approximation for a Stokes-Brinkman-type formulation for the eigenvalue problem in porous media
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908451511205888 |
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| author | Lepe, Felipe Rivera, Gonzalo Vellojin, Jesus |
| author_facet | Lepe, Felipe Rivera, Gonzalo Vellojin, Jesus |
| contents | We introduce a family of discontinuous Galerkin methods to approximate the eigenvalues and eigenfunctions of a Stokes-Brinkman type of problem based in the interior penalty strategy. Under the standard assumptions on the meshes and a suitable norm, we prove the stability of the discrete scheme. Due to the non-conforming nature of the method, we use the well-known non-compact operators theory to derive convergence and error estimates for the method. We present an exhaustive computational analysis where we compute the spectrum with different stabilization parameters with the aim of study its influence when the spectrum is approximated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11695 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Discontinuous Galerkin approximation for 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 We introduce a family of discontinuous Galerkin methods to approximate the eigenvalues and eigenfunctions of a Stokes-Brinkman type of problem based in the interior penalty strategy. Under the standard assumptions on the meshes and a suitable norm, we prove the stability of the discrete scheme. Due to the non-conforming nature of the method, we use the well-known non-compact operators theory to derive convergence and error estimates for the method. We present an exhaustive computational analysis where we compute the spectrum with different stabilization parameters with the aim of study its influence when the spectrum is approximated. |
| title | Discontinuous Galerkin approximation for 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/2507.11695 |