摘要：

In this talk, we consider two kinds of positivity-preserving finite element methods for solving the chemotaxis(-fluid) equations. In the first part, based on the flux-corrected transport technique, we develop a fully decoupled, linear, positivity-preserving and stable finite element scheme for solving the chemotaxis–fluid equations, in which we only need to solve several linearized sub-problems at each time step. The stability and error estimate of the scheme are proved. In the second part, based on the function transformation, we study a mass conservation and positivity-preserving finite element method for the chemotaxis equations. The stability and error estimate of the method are also proved. A series of numerical examples are shown to verify the theoretical predictions.

个人简介：

王坤，重庆大学数学与统计学院副教授，主要研究方向为偏微分方程数值解，具体包括复杂流体力学方程及其耦合问题、趋化方程的数值分析与模拟等，结果曾在SIAM Journal on Numerical Analysis，Mathematics of Computation等杂志上发表。