论文标题
线性弹性的混合方法的光谱分析
Spectral analysis of a mixed method for linear elasticity
论文作者
论文摘要
本文的目的是通过分段$（k+1）$（k+1）$，$ k $和$ k $和$ k+1）$（$ k \ geq 1 $）分析线性弹性特征值问题的混合方法。应力的数值特征功能是对称的。通过离散的$ h^1 $ - 数值位移的稳定性，我们证明了$ o（h^{k+2}）$近似与$ l^{2} $ - 正交指向精确位移的特征性问题的特征性问题的正交投影。因此，通过后处理，与常规方法相比，我们获得了本本本本本特征的精确位移的特征空间更好的近似。我们还证明，与泊松比相对于压力的特征功能的数值近似是自由锁定的。我们介绍了一种杂交，以将混合方法减少到一个凝结的特征问题上，并证明$ O（H^2）$初始近似（独立于非线性特征）的特征值（与弹性操作员的倒数无关），用于使用离散$ h^1 $ himeration $ o $ o（H），而$ o（H）仅使用$ o（H） 健康）状况。最后，我们报告了一些数值实验。
The purpose of this paper is to analyze a mixed method for linear elasticity eigenvalue problem, which approximates numerically the stress, displacement, and rotation, by piecewise $(k+1)$, $k$ and $(k+1)$-th degree polynomial functions ($k\geq 1$), respectively. The numerical eigenfunction of stress is symmetric. By the discrete $H^1$-stability of numerical displacement, we prove an $O(h^{k+2})$ approximation to the $L^{2}$-orthogonal projection of the eigenspace of exact displacement for the eigenvalue problem, with proper regularity assumption. Thus via postprocessing, we obtain a better approximation to the eigenspace of exact displacement for the eigenproblem than conventional methods. We also prove that numerical approximation to the eigenfunction of stress is locking free with respect to Poisson ratio. We introduce a hybridization to reduce the mixed method to a condensed eigenproblem and prove an $O(h^2)$ initial approximation (independent of the inverse of the elasticity operator) of the eigenvalue for the nonlinear eigenproblem by using the discrete $H^1$-stability of numerical displacement, while only an $O(h)$ approximation can be obtained if we use the traditional inf-sup condition. Finally, we report some numerical experiments.
