一、讲座主题

Finite Elements for Linear Elasticity: New and Renovated

二、时间

8月19日（周一）10:00-11：00

三、地点

中心校区知新楼B座1032报告厅

四、主讲人

刘江国

五、主讲人简介

刘江国，美国科罗拉多州立大学数学系教授，博士生导师。曾任美国工业与应用数学学会中部地区分会主席，现任Journal of Computational and Applied Mathematics 杂志编辑。主要研究兴趣为数值分析、科学计算及生物数学。已在SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing, Journal of Computational Physics 等杂志上发表论文40多篇。所主持的研究项目受美国国家自然科学基金资助。

六、摘要

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.

七、邀请人

高夫征 数学学院副教授

八、主办

山东大学数学学院