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High-order finite element method on a Vulanović–Bakhvalov mesh for a singularly perturbed convection–diffusion problem
Applied Mathematics Letters ( IF 2.9 ) Pub Date : 2022-09-28 , DOI: 10.1016/j.aml.2022.108457 Li-Bin Liu , Lei Xu , Yong Zhang
中文翻译:
Vulanović-Bakhvalov 网格的高阶有限元方法用于奇异摄动对流-扩散问题
更新日期:2022-09-28
Applied Mathematics Letters ( IF 2.9 ) Pub Date : 2022-09-28 , DOI: 10.1016/j.aml.2022.108457 Li-Bin Liu , Lei Xu , Yong Zhang
A th order () 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:
Vulanović-Bakhvalov 网格的高阶有限元方法用于奇异摄动对流-扩散问题
一个次订单() 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。