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arXiv · 2411.16641

On a Completely Discrete Discontinuous Galerkin Method for Incompressible Chemotaxis-Navier-Stokes Equations

Bikram Bir·Harsha Hutridurga·Amiya K. Pani
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Abstract

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.

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Bikram Bir, Harsha Hutridurga, Amiya K. Pani. 2024-11-25. On a Completely Discrete Discontinuous Galerkin Method for Incompressible Chemotaxis-Navier-Stokes Equations. https://doi.org/10.1007/s10915-025-03055-0

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