報告題目：Robust Nonconforming Finite Element Methods for the Strain Gradient Elasticity
報告人：黃學海 上海财經大學
時間：2024年 08月29日（星期四）10:40-11:25
地點: 正新樓209
校内聯系人：王瑞姝 wangrs_math@jlu.edu.cn
報告摘要：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.
報告人簡介：上海财經大學講席教授、博士研究生導師，研究方向為有限元方法。在Math. Comp.、SIAM J. Numer. Anal.、Numer. Math.、Math. Models Methods Appl. Sci.等國際期刊發表SCI論文四十多篇。正主持一項國家自然科學基金面上項目和上海市自然科學基金原創探索項目，主持完成國家自然科學基金面上項目、青年項目、數學天元項目和溫州市科技計劃項目各一項、浙江省自然科學基金項目兩項。獲中國計算數學學會優秀青年論文競賽優秀獎，博士學位論文被評為上海市研究生優秀成果(學位論文)。
