Error analysis for a fully-discrete finite element approximation of the unsteady $p(\cdot,\cdot)$-Stokes equations
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910769361190912 |
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| author | Berselli, Luigi C. Kaltenbach, Alex Ko, Seungchan |
| author_facet | Berselli, Luigi C. Kaltenbach, Alex Ko, Seungchan |
| contents | In this paper, we examine a fully-discrete finite element approximation of the unsteady $p(\cdot,\cdot)$-Stokes equations ($i.e.$, $p(\cdot,\cdot)$ is time- and space-dependent), employing a backward Euler step in time and conforming, discretely inf-sup stable finite elements in space. More precisely, we derive error decay rates for the vector-valued velocity field imposing fractional regularity assumptions on the velocity and the kinematic pressure. In addition, we carry out numerical experiments that confirm the optimality of the derived error decay rates in the case $p(\cdot,\cdot)\ge 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00849 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Error analysis for a fully-discrete finite element approximation of the unsteady $p(\cdot,\cdot)$-Stokes equations Berselli, Luigi C. Kaltenbach, Alex Ko, Seungchan Numerical Analysis 35J60, 35Q35, 65N15, 65N30, 76A05 In this paper, we examine a fully-discrete finite element approximation of the unsteady $p(\cdot,\cdot)$-Stokes equations ($i.e.$, $p(\cdot,\cdot)$ is time- and space-dependent), employing a backward Euler step in time and conforming, discretely inf-sup stable finite elements in space. More precisely, we derive error decay rates for the vector-valued velocity field imposing fractional regularity assumptions on the velocity and the kinematic pressure. In addition, we carry out numerical experiments that confirm the optimality of the derived error decay rates in the case $p(\cdot,\cdot)\ge 2$. |
| title | Error analysis for a fully-discrete finite element approximation of the unsteady $p(\cdot,\cdot)$-Stokes equations |
| topic | Numerical Analysis 35J60, 35Q35, 65N15, 65N30, 76A05 |
| url | https://arxiv.org/abs/2501.00849 |