报告题目：Robust finite elements for nearly incompressible strain gradient elasticity

报告人：廖钰蕾 博士

报告时间：2026年11月12日9:00

报告地点：数统学院210

邀请人：肖思

邀请单位：福州大学数学与统计学院

报告摘要：We establish new regularity results for the nearly incompressible strain gradient elasticity. The estimates are independent of both the microscopic length scale parameter and the Lame constant that accounts for the incompressiblity. Then we introduce a family of mixed finite elements that exhibit robustness for the nearly incompressible model. These elements are similar to the Taylor-Hood element in Stokes flows. We establish the discrete inf-sup condition for the mixed finite element pairs and demonstrate the optimal convergence rate for both smooth solution and the solution with boundary layer, which are robust in the incompressible limit. During the course of our numerical analysis, we propose a broken Hardy inequality for discontinuous finite element functions, which exhibits a logarithmic blow-up factor with respect to the mesh size.

报告人简介：廖钰蕾博士现为香港大学博士后。2024年在中国科学院数学与系统科学研究院取得博士学位，之后曾在新加坡国立大学从事博士后工作。主要研究方向为多尺度建模与模拟，数值偏微分方程，机器学习的理论与应用等。

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