A $k$th order ($k\ge 1$) finite element method on a Vulanović–Bakhvalov mesh is proposed for a singularly perturbed convection–diffusion problem. Some properties of the Vulanović–Bakhvalov mesh are derived. Based on these estimations and a new Lagrange interpolation technique, an optimal order of uniform convergence with respect to the perturbation parameter is proved. Numerical results are provided to demonstrate the theoretical findings.

中文翻译：

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Vulanović-Bakhvalov 网格的高阶有限元方法用于奇异摄动对流-扩散问题

一个$ķ$次订单（$ķ\ge 1$) Vulanović-Bakhvalov 网格上的有限元方法被提出用于奇异摄动对流-扩散问题。导出了 Vulanović-Bakhvalov 网格的一些属性。基于这些估计和新的拉格朗日插值技术，证明了关于扰动参数的一致收敛的最优阶。提供了数值结果来证明理论发现。