报告人：张上游教授(美国特拉华大学)

报告时间：2025年1月3日16:30-18:30

报告地点：数理楼245教室

报告摘要：In the very first paper on the finite element methods for Stokes and NavierStokes equations, Crouzeix and Raviart constructed the stable 2D and 3D P1nonconforming with P0 discontinuous mixed finite elements in 1972. Elevenyears later Fortin and Soulie proved the stability of 2D P2 nonconforming withP1 discontinuous mixed finite element and posted the question on its 3D version in 1985. The problem remains open for more than 40 years. In 2023, MathComp even published an erroneous paper on the 2D P2-P1 mixed finite element.In this talk, we show a correct way to enrich the conforming quadratic finite element space with seven quadratic nonconforming bubble functions. This spacialnonconforming quadratic finite element, combined with the discontinuous linear finite element on general tetrahedral grids, is inf-sup stable for solving theStokes equations. Consequently such a mixed finite element method producesoptimal-order convergent solutions for solving the stationary Stokes equations.This work closed a 40-year open problem since its 2D version was discovered.

报告人简介：张上游教授本科就读于1977级中国科技大学数学系，1988获得美国宾州州立大学数学博士,在美国普渡大学做了二年访问教授后一直在美国特拉华大学数学系任教授至今。张上游主要工作领域为计算数学有限元方法，高阶有限元、向量有限元和矩阵有限元的构造。已在计算数学的学术期刊上发表180篇有影响的学术论文。其中一篇关于Scott-Zhang(以其名字命名的算子在计算数学中广为引用)插值论文，在2010至2020年中几乎每年都进入所有数学论文引用百强，并在2018年《Math. Comp.》建刊75年大会上获引用率排名第二奖。