孙伟伟教授来澳门威尼斯举办系列学术讲座

报告人 ：孙伟伟 北京师范大学（珠海校区）教授

报告人简介 ：

西安交通大学学士，加拿大温莎大学博士，知名计算数学专家, 《Int. J. Numer. Anal. Model.》和《Numer. Math. TMA》编委，曾担任香港城市大学教授，2020 年 1 月加入 UIC。主要的研究方向是科学计算与数学模型，包括有高阶数值方法、数学模型、电磁场的计算等， 近几年针对非线性抛物问题提出了一套新的框架性的分析方法---无条件误差估计。在SIAM系列期刊上合作发表论文30余篇。

报告题目:New analysis of Galerkin FEMs for strongly coupled multi-physics systems

报告摘要：The talk focuses on optimal error estimates of FEMs for problems involving multi-physics fields, which are often described by nonlinear and strongly coupled parabolic/elliptic systems A question to be concerned is the optimality of numerical approximations for each components involved in the physical system. For many popular models, existing analysis may not be optimal for certain component. A typical example given in this talk is the incompressible miscible flow in porous media which has been widely used in many engineering areas, such as reservoir simulations and surface contaminant transport and remediation. The analysis done in the last several decades shows that classical Galerkin FEMs provide the numerical concentration of the accuracy $O(h_c^{r+1} + h^s_p)$ in $L^2$-norm, where $h_c$ and $h_p$ denotes the meshsize for the approximation to concentration and pressure, respectively. This analysis suggests to use a higher order finite element approximation to the pressure than that to the concentration in numerical simulations to achieve the best rate of convergence. But this is misleading since the error estimate is not optimal. In this talk, we introduce our recent work on new analysis of Galerkin-Galerkin methods to establish the optimal $L^2$ error estimate $O(h^{r+1} + h^{s+1})$ from which one can see that the best convergence rate can be achieved by taking the same order $(r=s$) approximation to the concentration and pressure. Clearly Galerkin FEMs with $r=s$ are less expensive in computation and easier for implementation. Numerical results for both two and three-dimensional models are presented to confirm our theoretical analysis. Finally, we extend our analysis to Galerkin-mixed methods to obtain optimal error estimates for each components.

报告时间 ：2020年10月16日上午10：00-12：00

报告地点 ：腾讯会议室：365 220 388