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arXiv · 2504.04357

Unconditionally optimal error Estimate of a linearized Second-order Fully Discrete Finite Element Method for the bioconvection flows with concentration dependent viscosity

Chenyang Li·Yuze Lu·Haibiao Zheng
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Abstract

In this paper, the coupled and decoupled BDF2 finite element discrete schemes are obtained for the time-dependent bioconvection flows problem with concentration dependent viscosity, which consisting of the Navier-Stokes equation coupled with a linear convection-diffusion equation modeling the concentration of microorganisms in a culture fluid. The unconditionally optimal error estimate for the velocity and concentration in $L^2$-norm and $H^1$-norm are proved by using finite element approximations in space and finite differences in time. Finally, the numerical results for different viscosity are showed to support the theoretical analysis.

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Chenyang Li, Yuze Lu, Haibiao Zheng. 2025-05-21. Unconditionally optimal error Estimate of a linearized Second-order Fully Discrete Finite Element Method for the bioconvection flows with concentration dependent viscosity. https://doi.org/10.4208/jcm.2601-m2025-0140

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