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Lecture on "Finite Elements for Linear Elasticity: New and Renovated"
DateandTime: 2019-08-07 17:35:29

Speaker:Jiangguo Liu, Professor, Colorado State University,US

Date:August 19, 2019

Time: 10:00-11:00 am

Location:Hall 1032, Block B, Zhixin Building, Central Campus

Sponsor:the School of Mathematics

Abstract:

It is well known that the continuous Galerkin finite elements suffer Poisson locking when applied to elasticity. In this talk, we first examine the suspicious behaviors of the classical Lagrangian elements in solving linear elasticity problems. A good remedy is to enrich the Lagrangian elements by edge/face-based bubble functions. This was motivated by the Bernardi-Raugel elements that were originally designed for Stokes flow. Then we move on to the novel weak Galerkin finite elements, which use vector-valued polynomial shape functions defined separately in element interiors and on edges/faces. The discrete weak gradients and divergences of these shape functions are reconstructed via integration by parts in matrix or scalar spaces that have desired approximation properties. Numerical results along with brief analysis will be presented to demonstrate the accuracy and efficiency of these renovated and novel finite elements. This talk is based on a series joint work with several collaborators.

Bio:

Liu Jiangguo is a professor doctoral tutor of mathematics at Colorado State University. He has served as Chairman of the Central Branch of the American Society of Industrial and Applied Mathematics and is currently the editor of the Journal of Computational and Applied Mathematics. His main research interests are numerical analysis, scientific computing, and biomathematics. More than 40 papers have been published in journals such as SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing, Journal of Computational Physics. Research projects that he hosted are funded by the National Natural Science Foundation of the United States.

For more information, please visit:

http://www.view.sdu.edu.cn/info/1020/121419.htm

Edited by:Liu Li




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