报告题目：Pressure-robust finite element methods for Stokes and Stokes-Darcy problems

报告人：芮洪兴

报告时间：10月14日  3：45

报告地点：五教5101

摘要：

In this talk, we first propose a divergence free discretization method for the Stokes equations based on P1⊕RT0 - P0 on general simplicial meshes in 2D/3D, which yields an divergence-free and pressure independent velocity approximation with optimal order. The global number of the degrees of freedom is the same as the low order Bernardi-Raugel element. A priori error and a posterior error estimate are obtained. Then we present a pressure-robust mixed element method for the coupled Stokes-Darcy problems using P1⊕RT0 and RT0 elements on Stokes and Darcy regions respectively. Applications to solve the Stokes optimal control problem, the interface problems, the high order divergence-free element are briefly introduced. Numerical experiments illustrate the robustness and accuracy of our method.

简介：

芮洪兴，山东大学二级教授、博士生导师，主要从事偏微分方程数值方法、多孔介质渗流及流体的数值计算及应用研究。在SINUM，Numer Math，Math Comp，M3AS,CMAME，JCP，JFM等顶级期刊发表多篇高水平论文。主持国家自然科学基金重点项目等，获山东省自然科学一等奖、二等奖、教育部自然科学二等奖等。现任山东工业与应用数学学会副理事长、山东数学会计算数学专委会主任。