弹性问题线性常数元稳定化方法

A stabilized linear-constant finite element method for elasticity problem

摘要:

运用混合有限元法求解弹性问题时，由于LBB条件的限制，使得实际工程运用中常用的线性/常数元无法应用。为了克服这一困难，本文将Bochev-Dohrmann-Gunzburger稳定性方法应用在弹性问题上，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。

Abstract:

The commonly 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 Bochev-Dohrmann-Gunzburger method. We add a consistent term and projection-type stabilization term, which can effectively bypass the inf-sup condition. The advantages of our method are: they do not depend on the space dimension, do not require calculation of higher order derivatives or edge-based data structures.