We consider fourth order singularly perturbed eigenvalue problems in one-dimension and the approximation of their solution by the $h$ version of the Finite Element Method (FEM). In particular, we use piecewise Hermite polynomials of degree $p\geq 3$ defined on an {\emph{exponentially graded}} mesh. We show that the method converges uniformly, with respect to the singular perturbation parameter, at the optimal rate when the error in the eigenvalues is measured in absolute value and the error in the eigenvectors is measured in the energy norm. We also illustrate our theoretical findings through numerical computations for the case $p=3$.

翻译：我们认为,在单层中,第四种单层奇相扰动的乙基值问题,以及其解决办法的近似值,即以美元表示的 " 精度元素法 " (FEM)的绝对值和 " 精度元元素法 " (FEM)的近似值。特别是,我们使用在 phemph{Expentientially dicled ⁇ mesh 上定义的纯度三美元半热量多元数。我们表明,在单层扰动参数方面,该方法一致一致,以最佳速率,即对精度值的误差以绝对值衡量,对精度元素的误差以能源规范衡量。我们还通过对案例的数值计算来说明我们的理论结论,即$p=3美元。