Fully decoupled, linear, positivity-preserving and unconditionally stable scheme for the chemotaxis–Stokes equations
报告题目：Fully decoupled, linear, positivity-preserving and unconditionally stable scheme for the chemotaxis–Stokes equations
In this talk, we develop a fully decoupled, linear, positivity-preserving and unconditionally stable finite element scheme for solving the chemotaxis–Stokes equations, which describe the biological chemotaxis phenomenon in the fluid environment. To deal with the strong coupling of the problem, we first consider a fully decoupled and linear semi-discrete scheme, in which we only need to solve several linearized sub-problems at each time step for the velocity, pressure, oxygen concentration and cell density, respectively. Then, based on the linear finite element method for the spatial discretization, the flux-corrected transport algorithm is extended to the oxygen concentration and cell density sub-problems to preserve their positivity. Moreover, the unconditional stability and error estimate of the scheme is proved. Finally, we show a series of numerical examples to verify the theoretical predictions.
王坤，重庆大学数学与统计学院副教授、硕士生导师。毕业于西安交通大学，获理学博士学位，并曾在加拿大Alberta大学从事博士后研究。主要从事偏微分方程数值解方面的研究，包括复杂流体力学方程、趋化模型和散射问题的数值分析与模拟等，其结果曾在SIAM Journal of Numerical Analysis, Journal of Computational Physics，Computer Methods in Applied Mechanics and Engineering，Communications in Computational Physics等杂志上发表。