Finite element discretization of the steady, generalized Navier-Stokes equations for small shear stress exponents
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913097591029760 |
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| author | Kaltenbach, Alex Jeßberger, Julius |
| author_facet | Kaltenbach, Alex Jeßberger, Julius |
| contents | A finite element (FE) discretization for the steady, incompressible, fully inhomogeneous, generalized Navier-Stokes equations is proposed. By the method of divergence reconstruction operators, the formulation is valid for all shear stress exponents $p > \tfrac{2d}{d+2}$. The Dirichlet boundary condition is imposed strongly, using any discretization of the boundary data which converges at a sufficient rate. $\textit{A priori}$ error estimates for the velocity vector field and kinematic pressure are derived and numerical experiments are conducted. These confirm the quasi-optimality of the $\textit{a priori}$ error estimate for the velocity vector field. The $\textit{a priori}$ error estimates for the kinematic pressure are quasi-optimal if $p \leq 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15731 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite element discretization of the steady, generalized Navier-Stokes equations for small shear stress exponents Kaltenbach, Alex Jeßberger, Julius Numerical Analysis 35J60, 35Q35, 65N12, 65N15, 65N30, 76A05 A finite element (FE) discretization for the steady, incompressible, fully inhomogeneous, generalized Navier-Stokes equations is proposed. By the method of divergence reconstruction operators, the formulation is valid for all shear stress exponents $p > \tfrac{2d}{d+2}$. The Dirichlet boundary condition is imposed strongly, using any discretization of the boundary data which converges at a sufficient rate. $\textit{A priori}$ error estimates for the velocity vector field and kinematic pressure are derived and numerical experiments are conducted. These confirm the quasi-optimality of the $\textit{a priori}$ error estimate for the velocity vector field. The $\textit{a priori}$ error estimates for the kinematic pressure are quasi-optimal if $p \leq 2$. |
| title | Finite element discretization of the steady, generalized Navier-Stokes equations for small shear stress exponents |
| topic | Numerical Analysis 35J60, 35Q35, 65N12, 65N15, 65N30, 76A05 |
| url | https://arxiv.org/abs/2408.15731 |