论文标题
简化的Galbrun方程的强大有限元离散化
Robust finite element discretizations for a simplified Galbrun's equation
论文作者
论文摘要
在为Galbrun方程寻找鲁棒离散方法的挑战性任务的驱动下，我们研究了在简化的方程式上，针对不同有限元元素方案的稳定性和鲁棒性的不同方面的条件。考虑的PDE是二阶不确定的矢量-PDE，如果仅考虑Galbrun方程的最高级条款，则仍然存在。稳定性的关键属性是Helmholtz型分解，它在Galbrun方程与Stokes稳定离散和几乎不可压缩的线性弹性问题之间产生了牢固的联系。
Driven by the challenging task of finding robust discretization methods for Galbrun's equation, we investigate conditions for stability and different aspects of robustness for different finite element schemes on a simplified version of the equations. The considered PDE is a second order indefinite vector-PDE which remains if only the highest order terms of Galbrun's equation are taken into account. A key property for stability is a Helmholtz-type decomposition which results in a strong connection between stable discretizations for Galbrun's equation and Stokes and nearly incompressible linear elasticity problems.
