弹性问题的线性常数元稳定化方法  

Stabilized linear-constant finite element method for elasticity problem

作　　者：刘书琳[1] 胡戎 

机构地区：[1]四川大学数学学院,成都610064 [2]川庆地质勘探开发研究院,成都610051

出　　处：《四川大学学报（自然科学版）》2017年第3期447-451,共5页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金11271273

摘　　要：当运用混合有限元法求解弹性问题时,LBB条件的限制使得工程应用中常用的线性/常数元无法应用.为了克服这一困难,本文将Bochev-Dohrmann-Gunzburger稳定性方法应用于弹性问题,通过增加新的投影稳定项和相容稳定项,提出了一种稳定化混合有限元方法.该方法的优点在于不依赖空间维数和单元形状,也不需要计算高阶导数或边界跳跃量.The extensively used linear / constant element cannot be applied in solving elasticity problem because it dissatisfy the LBB condition. In this paper, we derive a stabilization scheme for elasticity problem based on the Bochev-Dohrmann-Gunzburger method by adding a consistent term and projection-type stabilization term, which can effectively bypass the inf-sup condition. The advantage a of our method lies in that it does not depend on the space dimension and require calculation of higher order derivatives or edge-based data structures.

关 键 词：弹性问题 弱inf-sup条件 稳定化 

分 类 号：O241.82[理学—计算数学]