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

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发表日期：

2025年9月20日

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Bikram Bir,
Harsha Hutridurga,
Amiya K. Pani

摘要

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 is applied in the temporal direction to obtain a completely discrete scheme. With the help of a new projection, optimal error estimates in $L^2$ $L^{2}$ and $H^1$ $H^{1}$ -norms for the cell density, the concentration of chemical substances and the fluid velocity are derived. Further, optimal error bound in $L^2$ $L^{2}$ -norm for the fluid pressure is established. Finally, some numerical simulations are performed, whose results confirm the theoretical findings.