Keynote Speaker: Liu Jianguo

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.

Speaker Introduction:

Liu Jianguo, professor of Department of Mathematics of Colorado State University, and doctoral tutor, served as Chairman of the Central Region Branch of the Society for Industrial and Applied Mathematics (SIAM), and is currently the editor of the Journal of Computational and Applied Mathematics. He mainly studies numerical analysis, scientific computing, and biomathematics, and has published more than 40 papers in SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing, Journal of Computational Physics, etc. The research projects hosted are funded by the National Science Foundation.

Inviter:

Gao Fuzheng, associate professor of School of Mathematics

Time:

10:00-11:00 on August 19 (Monday)

Location:

Hall 1032, Block B, Zhixin Building, Central Campus

Hosted by: School of Mathematics, Shandong University