时间：2018年11月22日 上午10:30—11:30
地点：数学楼202讨论室
题目：An introduction of weak Galerkin finite element methods and a third order convergence P2 WG for biharmonic equations
摘要：We introduce generalized functions and generalized derivatives. By a finite dimensional approximation, the generalized derivatives are the so-called weak gradients. Consequently we introduce the weak Galerkin finite element methods. We discuss the equivalence and differences between WG and other finite element methods.
As an example showing the flexibility and the advantage of WG, we construct a special P2 WG finite element which is order 3 convergent in L2 for solving biharmonic equations, while it is not possible for all other P2 finite method methods. Jun Hu proved an order 2 lower bound in L2 for conforming and nonconforming P2 finite elements when solving biharmonic equations.
个人简介：张上游教授本科就读于1977级中国科技大学数学系，获1988年美国宾州州立大学数学博士。在美国普渡大学任访问助理教授两年后一直在美国特拉华大学任助理教授和副教授至今。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。在计算数学杂志上发表了74篇论文（其中有顶级杂志《Math Comp》文章11篇）和7篇会议论文。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，在过去10年中多次被《数学评论》评为数学论文引用百强，并在2018年《Math Comp》建刊75年大会上获奖。
