A Construction of C^r Conforming Finite Element Spaces in Any Dimension
Overview
This talk proposes a construction of Cr conforming finite element spaces with arbitrary r in any dimension. It is shown that if k≥2d r+1 the space Pk of polynomials of degree not greater than k can be taken as the shape function space of Cr finite element spaces in d dimensions. This is the first work on constructing such Cr conforming finite elements in any dimension in a unified way.
Presenters
Jun Hu
Brief Biography
Jun Hu is a Professor of Mathematics at Peking University. His main research interest is in finite element methods of partial differential equations, including mixed finite element methods for problems arising from mechanics, finite element methods for partial differential equations eigenvalue problems and high order problems, adaptive finite element methods, and nonlinear approximations. His main works include the construction of optimal, easy-to-implement, highly efficient and perfectly matched mixed finite element methods for elasticity, the development of the first symmetry-preserving mixed finite element methods for the linearized Einstein-Bianchi system, and the first universal construction of conforming finite elements on simplicial grids for 2(r+1)-th order elliptic partial differential equations in any dimension for any nonnegative integer r. He has published over 90 publications in peer-reviewed journals, and serves as President of the Beijing Society of Computational Mathematics and Member of the Executive Committee of Chinese Mathematical Society, one of managing editors of journal Advances in Applied Mathematics and Mechanics, an editor of five journals: Computational Methods in Applied Mathematics, Computer and Mathematics with Applications, CSIAM Transactions on Applied Mathematics, and Journal of Computational Mathematics, Mathematical Theory and Applications. He is the recipient of First prize of the Natural Science Award from the Ministry of Education in 2022, the Feng Kang Prize of Scientific Computing in 2019, National Science Fund for Distinguished Young Scholar of PR China in 2016, the first Youth Innovation prize of China Society for Computational Mathematics in 2015 and the National Excellent Doctoral Dissertation of PR China in 2006, and a former Alexander von Humboldt Research Fellow of Alexander von Humboldt Foundation of Germany in 2004.