讲座主题：Taylor-Hood like finite elements for nearly incompressible strain gradient elasticity problems

专家姓名：明平兵

工作单位：中国科学院数学与系统科学研究院

讲座时间：2022年11月9日 14:30-16:30

讲座地点：腾讯会议：138-413-381

主办单位：9728太阳集团数学与信息科学学院

内容摘要：

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.

主讲人介绍：

明平兵，中国科学院数学与系统科学研究院研究员，担任科学与工程计算国家重点实验室副主任。主要从事固体多尺度建模、模拟及多尺度算法的研究。于2014年获得国家杰出青年基金。