报告题目：Robust Nonconforming Finite Element Methods for the Strain Gradient Elasticity
报告人：黄学海 上海财经大学
时间：2024年 08月29日（星期四）10:40-11:25
地点: 正新楼209
校内联系人：王瑞姝 wangrs_math@jlu.edu.cn
报告摘要：Robust low-order finite element methods are developed for the strain gradient elasticity (SGE) model. The uniform regularity of the SGE model is derived under two reasonable assumptions. (1) First we design a robust nonconforming mixed finite element method. A lower order $C^0$-continuous $H^2$-nonconforming finite element is constructed for the displacement field through enriching the quadratic Lagrange element with bubble functions. This together with the linear Lagrange element is exploited to discretize a mixed formulation of the SGE model. The sharp and uniform error estimates with respect to both the small size parameter $\iota$ and the Lam\'{e} coefficient are achieved. (2) Then we develop an optimal and robust low-order nonconforming finite element method for the primal formulation. An $H^2$-nonconforming quadratic vector-valued finite element in arbitrary dimension is constructed, which together with an $H^1$- nonconforming scalar finite element and the Nitsche's technique, is applied for solving the SGE model. The resulting nonconforming finite element method is optimal and robust with respect to the Lam\'{e} coefficient $\lambda$ and the size parameter $\iota$, as confirmed by numerical results. Additionally, nonconforming finite element discretization of the smooth Stokes complex in two and three dimensions is devised.
报告人简介：上海财经大学讲席教授、博士研究生导师，研究方向为有限元方法。在Math. Comp.、SIAM J. Numer. Anal.、Numer. Math.、Math. Models Methods Appl. Sci.等国际期刊发表SCI论文四十多篇。正主持一项国家自然科学基金面上项目和上海市自然科学基金原创探索项目，主持完成国家自然科学基金面上项目、青年项目、数学天元项目和温州市科技计划项目各一项、浙江省自然科学基金项目两项。获中国计算数学学会优秀青年论文竞赛优秀奖，博士学位论文被评为上海市研究生优秀成果(学位论文)。
