On a Completely Discrete Discontinuous Galerkin Method for Incompressible Chemotaxis-Navier-Stokes Equations
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| Format: | Preprint |
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2024
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| _version_ | 1866914474592567296 |
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| author | Bir, Bikram Hutridurga, Harsha Pani, Amiya K. |
| author_facet | Bir, Bikram Hutridurga, Harsha Pani, Amiya K. |
| contents | This paper deals with a fully discrete numerical scheme for the incompressible Chemotaxis(Keller-Segel)-Navier-Stokes system. Based on a discontinuous Galerkin finite element scheme in the spatial directions, a semi-implicit first-order finite difference method in the temporal direction is applied to derive a completely discrete scheme. With the help of a new projection, optimal error estimates in $L^2$ and $H^1$-norms for the cell density, the concentration of chemical substances and the fluid velocity are derived. Further, optimal error bound in $L^2$-norm for the fluid pressure is obtained. Finally, some numerical simulations are performed, whose results confirm the theoretical findings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_16641 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a Completely Discrete Discontinuous Galerkin Method for Incompressible Chemotaxis-Navier-Stokes Equations Bir, Bikram Hutridurga, Harsha Pani, Amiya K. Numerical Analysis 65M60, 65M15, 35Q30 This paper deals with a fully discrete numerical scheme for the incompressible Chemotaxis(Keller-Segel)-Navier-Stokes system. Based on a discontinuous Galerkin finite element scheme in the spatial directions, a semi-implicit first-order finite difference method in the temporal direction is applied to derive a completely discrete scheme. With the help of a new projection, optimal error estimates in $L^2$ and $H^1$-norms for the cell density, the concentration of chemical substances and the fluid velocity are derived. Further, optimal error bound in $L^2$-norm for the fluid pressure is obtained. Finally, some numerical simulations are performed, whose results confirm the theoretical findings. |
| title | On a Completely Discrete Discontinuous Galerkin Method for Incompressible Chemotaxis-Navier-Stokes Equations |
| topic | Numerical Analysis 65M60, 65M15, 35Q30 |
| url | https://arxiv.org/abs/2411.16641 |