二维奇异扰动对流扩散方程的 Vulanović-Bakhvalov 网格上有限元方法的均匀收敛性

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications Pub Date : 2025-04-15 DOI:10.1016/j.camwa.2025.04.007

Xianyang Zhao, Jin Zhang

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引用次数: 0

摘要

研究了Vulanović-Bakhvalov网格上任意阶有限元方法的一致收敛性。我们精心设计了一种新的基于指数层结构的插值方法，既克服了网格步宽带来的困难，又保证了Dirichlet边界条件。我们成功地证明了最优阶在能量范数上的一致收敛性。数值实验结果有力地验证了我们的分析。

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Uniform convergence of finite element method on Vulanović-Bakhvalov mesh for singularly perturbed convection–diffusion equation in 2D

This paper investigates the uniform convergence of arbitrary order finite element methods on Vulanović-Bakhvalov mesh. We carefully design a new interpolation based on exponential layer structure, which not only overcomes the difficulties caused by the mesh step width, but also ensures the Dirichlet boundary condition. We successfully demonstrate the uniform convergence of the optimal order in the energy norm. The results of numerical experiments strongly validate our analysis.

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来源期刊

Computers & Mathematics with Applications 工程技术-计算机：跨学科应用

CiteScore

5.10

自引率

10.30%

发文量

396

审稿时长

9.9 weeks

期刊介绍： Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs).