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

2024/11/25 by Bir, Bikram, Hutridurga, Harsha, Pani, Amiya K. · 1 citation
#35Q30 #65M15 #65M60 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2411.16641

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 L² and H¹-norms for the cell density, the concentration of chemical substances and the fluid velocity are derived. Further, optimal error bound in L²-norm for the fluid pressure is obtained. Finally, some numerical simulations are performed, whose results confirm the theoretical findings.

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• Fully discrete finite element approximation for the projection method to solve the Chemotaxis-Fluid System

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