报告题目：A family of triangular nonconforming finite elements for the 2mth order differential equations

报告人：张上游 教授

报告时间：2016年11月29日（周二）16：00

报告地点：清水河校区主楼A1-512室

报告摘要：

The conforming and nonconforming P1 finite elements are the lowest order finite elements for solving 2nd order elliptic equations. For the (4th order) biharmonic equation,  the P2 Morley finite element is the lowest order H2-nonconforming element on the triangular grid. The Argyris P5 finite element is the lowest order conforming element. But for the 6th order (and 2m order) equation, P3 (and Pm) nonconforming element does not exist. For the 2m-th order equation, the lowest conforming element is of polynomials of degree 4m plus 1.

In this work, we construct a family of nonconforming Hm finite element of degree 2m minus 3. The consistent error is estimated and the optimal order of convergence is proven. Numerical tests on the new elements for solving tri-harmonic, 4-harmonic, 5-harmonic and 6-harmonic equations are presented, verifying the theory.  

报告人简介：

张上游毕业于中国科技大学数学系七七级。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。 

张上游主要工作在多重网格法和有限元构造。 共发表60多篇学术论文和10篇会议论文。其中一篇论文在过去十五年一直都在数学论文引用率百强之内。