首页|THE SUPERCLOSENESS OF THE FINITE ELEMENT METHOD FOR A SINGULARLY PERTURBED CONVECTION-DIFFUSION PROBLEM ON A BAKHVALOV-TYPE MESH IN 2D

THE SUPERCLOSENESS OF THE FINITE ELEMENT METHOD FOR A SINGULARLY PERTURBED CONVECTION-DIFFUSION PROBLEM ON A BAKHVALOV-TYPE MESH IN 2D

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For singularly perturbed convection-diffusion problems,supercloseness analysis of the finite element method is still open on Bakhvalov-type meshes,especially in the case of 2D.The difficulties arise from the width of the mesh in the layer adjacent to the transition point,resulting in a suboptimal estimate for convergence.Existing analysis techniques cannot handle these difficulties well.To fill this gap,here a novel interpolation is designed delicately for the smooth part of the solution,bringing about the optimal supercloseness result of almost order 2 under an energy norm for the finite element method.Our theoretical result is uniform in the singular perturbation parameter ε and is supported by the numerical experiments.

singularly perturbedconvection-diffusionfinite element methodsuperclose-nessBakhvalov-type mesh

张春晓、张进

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School of Mathematics and Statistics,Shandong Normal University,Jinan 250014,China

National Natural Science Foundation of ChinaShandong Provincial Natural Science Foundation of ChinaShandong Provincial Natural Science Foundation of ChinaShandong Provincial Natural Science Foundation of China

11771257ZR2023YQ002ZR2023MA007ZR2021MA004

2024

10.1007/s10473-024-0421-7

数学物理学报(英文版)
中科院武汉物理与数学研究所

数学物理学报(英文版)

CSTPCD
影响因子：0.256
ISSN：0252-9602
年,卷(期)：2024.44(4)