标题： 关于浓度依赖黏性生物对流流动的线性化二阶全离散有限元法的无条件最优误差估计 显示英文标题

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

摘要： 本文针对浓度依赖粘性的时间相关生物对流流动问题，获得了耦合和解耦的二阶向后差分（BDF2）有限元离散格式，该问题由与刻画培养液中微生物浓度的线性对流扩散方程耦合的Navier-Stokes方程组成。 通过空间上的有限元逼近和时间上的有限差分离散方法，证明了速度和浓度在$L^2$-范数和$H^1$-范数下的无条件最优误差估计。 最后，展示了不同粘性情况下的数值结果以支持理论分析。 显示英文摘要

摘要： 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.