A polytopal discontinuous Galerkin method for the pseudo-stress formulation of the unsteady Stokes problem
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915647381831680 |
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| author | Antonietti, Paola F. Botti, Michele Cancrini, Alessandra Mazzieri, Ilario |
| author_facet | Antonietti, Paola F. Botti, Michele Cancrini, Alessandra Mazzieri, Ilario |
| contents | This work aims to construct and analyze a discontinuous Galerkin method on polytopal grids (PolydG) to solve the pseudo-stress formulation of the unsteady Stokes problem. The pseudo-stress variable is introduced due to the growing interest in non-Newtonian flows and coupled interface problems, where stress assumes a fundamental role. The space-time discretization of the problem is achieved by combining the PolydG approach with the implicit theta-method time integration scheme. For both the semi- and fully-discrete problems we present a detailed stability analysis. Moreover, we derive convergence estimates for the fully discrete space-time discretization. A set of verification tests is presented to verify the theoretical estimates and the application of the method to cases of engineering interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08760 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A polytopal discontinuous Galerkin method for the pseudo-stress formulation of the unsteady Stokes problem Antonietti, Paola F. Botti, Michele Cancrini, Alessandra Mazzieri, Ilario Numerical Analysis 65M12, 65M60 This work aims to construct and analyze a discontinuous Galerkin method on polytopal grids (PolydG) to solve the pseudo-stress formulation of the unsteady Stokes problem. The pseudo-stress variable is introduced due to the growing interest in non-Newtonian flows and coupled interface problems, where stress assumes a fundamental role. The space-time discretization of the problem is achieved by combining the PolydG approach with the implicit theta-method time integration scheme. For both the semi- and fully-discrete problems we present a detailed stability analysis. Moreover, we derive convergence estimates for the fully discrete space-time discretization. A set of verification tests is presented to verify the theoretical estimates and the application of the method to cases of engineering interest. |
| title | A polytopal discontinuous Galerkin method for the pseudo-stress formulation of the unsteady Stokes problem |
| topic | Numerical Analysis 65M12, 65M60 |
| url | https://arxiv.org/abs/2408.08760 |