论文标题
Bakhvalov型网眼上有限元法的最佳均匀收敛顺序
Optimal order of uniform convergence for finite element method on Bakhvalov-type meshes
论文作者
论文摘要
我们建议对$ K $ TH订单（$ K \ ge 1 $）有限元方法进行新的收敛分析，该方法应用于Bakhvalov-type网格网格，以奇异地扰动的两点边界价值问题。引入了一种新颖的插值，它具有简单的结构，易于概括。通过这种插值，我们证明了相对于扰动参数的最佳收敛阶。 数值实验说明了这些理论结果。
We propose a new analysis of convergence for a $k$th 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.
