Error analysis for a finite element approximation of the steady $p(\cdot)$-Navier-Stokes equations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909389734019072 |
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| author | Berselli, Luigi C. Kaltenbach, Alex |
| author_facet | Berselli, Luigi C. Kaltenbach, Alex |
| contents | In this paper, we examine a finite element approximation of the steady $p(\cdot)$-Navier-Stokes equations ($p(\cdot)$ is variable dependent) and prove orders of convergence by assuming natural fractional regularity assumptions on the velocity vector field and the kinematic pressure. Compared to previous results, we treat the convective term and employ a more practicable discretization of the power-law index $p(\cdot)$. Numerical experiments confirm the quasi-optimality of the $\textit{a priori}$ error estimates (for the velocity) with respect to fractional regularity assumptions on the velocity vector field and the kinematic pressure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00534 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Error analysis for a finite element approximation of the steady $p(\cdot)$-Navier-Stokes equations Berselli, Luigi C. Kaltenbach, Alex Numerical Analysis 35J60, 35Q35, 65N15, 65N30, 76A05 In this paper, we examine a finite element approximation of the steady $p(\cdot)$-Navier-Stokes equations ($p(\cdot)$ is variable dependent) and prove orders of convergence by assuming natural fractional regularity assumptions on the velocity vector field and the kinematic pressure. Compared to previous results, we treat the convective term and employ a more practicable discretization of the power-law index $p(\cdot)$. Numerical experiments confirm the quasi-optimality of the $\textit{a priori}$ error estimates (for the velocity) with respect to fractional regularity assumptions on the velocity vector field and the kinematic pressure. |
| title | Error analysis for a finite element approximation of the steady $p(\cdot)$-Navier-Stokes equations |
| topic | Numerical Analysis 35J60, 35Q35, 65N15, 65N30, 76A05 |
| url | https://arxiv.org/abs/2311.00534 |