講座主題：Taylor-Hood like finite elements for nearly incompressible strain gradient elasticity problems
專家姓名：明平兵
工作單位：中國科學院數學與系統科學研究院
講座時間：2022年11月9日 14:30-16:30
講座地點：騰訊會議：138-413-381
主辦單位：煙臺大學數學與信息科學學院
內容摘要：
We propose a family of mixed finite elements that are robust for the nearly incompressible strain gradient model, which is a fourth-order singular perturbed elliptic system. The element is similar to Taylor and P. Hood, in the Stokes flow. Using a uniform discrete B-B inequality for the mixed finite element pairs, we show the optimal rate of convergence that is robust in the incompressible limit. By a new regularity result that is uniform in both the materials parameter and the incompressibility, we prove the method converges with 1/2 order to the solution with strong boundary layer effects. Moreover, we estimate the convergence rate of the numerical solution to the unperturbed second-order elliptic system. Numerical results for both smooth solutions and the solutions with sharp layers confirm the theoretical prediction. We shall also discuss FEM approximation of this problem with double traction boundary conditions. This is a joint work with Yulei Liao and Yun Xu.
主講人介紹：
明平兵，中國科學院數學與系統科學研究院研究員，擔任科學與工程計算國家重點實驗室副主任。主要從事固體多尺度建模、模擬及多尺度算法的研究。于2014年獲得國家杰出青年基金。
