报告题目：Stabilizations for Stokes problem with pressure boundary condition

报 告 人：段火元教授（武汉大学）

报告时间：2021年9月24日  15:00-16:00

报告地点：腾讯会议（701525275）

报告摘要：

The Stokes problem with pressure boundary conditions are nonstandard and have numerous applications in realistic world, e.g., computational biomedical science and computational electromagnetism. There have been many finite element methods for incompressible flows, such as inf-sup stable method, stabilized method.Unfortunately, however,not all the methods are applicable to the pressure boundary condition.For instance, the well-known Mini element and all the divergence-free elements fail, in general, leading to wrong convergent finite element solutions whenever the velocity solution is singular not being Dirichlet integrable. In practice, the velocity solution has such singularity very often. This is mainly due to the nonsmooth domain. In this talk, I will report a new stabilized finite element method. The new method can correctly solve the Stokes problem with the pressure boundary condition,with a correct convergentfinite element solution to singular velocity solution. Numerical results illustrate the performance of the new method.

报告人简介：

段火元，武汉大学数学与统计学院教授、博士生导师。研究方向：偏微分方程数值解、有限元方法、多重网格算法、自适应算法、预处理迭代算法；随机微分方程的数值方法及应用；图像处理的数值方法；反问题数值方法。在国内外学术期刊发表学术论文近50篇，包括国际著名期刊如SIAM Journal On Numerical Analysis, Mathematicsof Computation, Numerische Mathematik, Computer Methods in Applied Mechanics andEngineering, Journal of Computational Physics,IMA Journal of Numerical Analysis等。