We propose a new analysis of convergence for a kth order (\(k\ge 1\)) finite element method, which is applied on Bakhvalov-type meshes to a singularly perturbed two-point boundary value problem. A novel interpolant is introduced, which has a simple structure and is easy to generalize. By means of this interpolant, we prove an optimal order of uniform convergence with respect to the perturbation parameter. Numerical experiments illustrate these theoretical results.

中文翻译：

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Bakhvalov型网格上有限元方法的一致收敛的最优阶

我们提出了一种针对k阶（\（k \ ge 1 \））有限元方法的收敛性的新分析，该方法应用于Bakhvalov型网格上的奇异摄动两点边值问题。介绍了一种新颖的插值器，结构简单，易于推广。通过该插值，我们证明了关于扰动参数的均匀收敛的最优阶。数值实验说明了这些理论结果。