主题：Analysis of hybrid stress finite element and finite volume methods

报告题目：Analysis of hybrid stress finite element and finite volume methods for elasticity

报告人：谢小平（四川大学数学学院/长江数学中心教授、博导）

时间：2011.6.25（周六）上午10点，下午2点

地点：信息系会议室（数统大楼5楼）

内容简介：

This talk includes two parts:

The first part focuses on uniform convergence and a posteriori error estimation for assumed stress hybrid finite element methods. Assumed stress hybrid methods are known to improve the performance of standard displacement-based finite elements and are widely used in computational mechanics. The methods are based on the Hellinger-Reissner variational principle for the displacement and stress variables. This work analyzes two existing 4-node hybrid stress quadrilateral elements due to Pian and Sumihara [Int. J. Numer. Meth. Engng, 1984] and due to Xie and Zhou [Int. J. Numer. Meth. Engng, 2004], which behave robustly in numerical benchmark tests. For the finite elements, the isoparametric bilinear interpolation is used for the displacement approximation, while different piecewise-independent 5-parameter modes are employed for the stress approximation.

We show that the two schemes are free from Poisson-locking, in the sense that the error bound in the a priori estimate is independent of the relevant Lame constant $\lambda$. We also establish the equivalence of the methods to two assumed enhanced strain schemes. Finally, we derive reliable and efficient residual-based a posteriori error estimators for the stress in $L^2$-norm and the displacement in $H^1$-norm, and verify the theoretical results by some numerical experiments.

The second part is to discuss a hybrid stress finite volume method for elasticity equations. In the approach, we use a finite volume formulation for the equilibrium equation, and a hybrid stress quadrilateral finite element discretization for the constitutive equation with continuous piecewise isoparametric bilinear displacement interpolation and two types of stress approximation modes. We show the method is free from Poisson-locking. Numerical experiments confirm the theoretical results.

报告人简介；

谢小平， 四川大学数学学院/长江数学中心教授、博导。1989年——1996年于四川大学数学系读本科和研究生。96年留校任教。2000年博士毕业于中国航空工业631研究所。2004年评教授。2007年入选教育部“新世纪优秀人才支持计划”。2008年获德国洪堡基金资助。 现为中国计算数学学会第八届理事会常务理事，《高等学校计算数学学报》编委，中国计算物理学会理事。

主要研究领域：偏微分方程数值解、有限元法