An adaptive space-time method for nonlinear poroviscoelastic flows with discontinuous porosities
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914004630241280 |
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| author | Bachmayr, Markus Boisserée, Simon |
| author_facet | Bachmayr, Markus Boisserée, Simon |
| contents | This paper is concerned with a space-time adaptive numerical method for instationary porous media flows with nonlinear interaction between porosity and pressure, with focus on problems with discontinuous initial porosities. A convergent method that yields computable error bounds is constructed by a combination of Picard iteration and a least-squares formulation. The adaptive scheme permits spatially variable time steps, which in numerical tests are shown to lead to efficient approximations of solutions with localized porosity waves. The method is also observed to exhibit optimal convergence with respect to the total number of spatio-temporal degrees of freedom. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_13420 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An adaptive space-time method for nonlinear poroviscoelastic flows with discontinuous porosities Bachmayr, Markus Boisserée, Simon Numerical Analysis This paper is concerned with a space-time adaptive numerical method for instationary porous media flows with nonlinear interaction between porosity and pressure, with focus on problems with discontinuous initial porosities. A convergent method that yields computable error bounds is constructed by a combination of Picard iteration and a least-squares formulation. The adaptive scheme permits spatially variable time steps, which in numerical tests are shown to lead to efficient approximations of solutions with localized porosity waves. The method is also observed to exhibit optimal convergence with respect to the total number of spatio-temporal degrees of freedom. |
| title | An adaptive space-time method for nonlinear poroviscoelastic flows with discontinuous porosities |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2409.13420 |