Supercloseness of linear streamline diffusion finite element method on Bakhvalov-type mesh for singularly perturbed convection-diffusion equation in 1D

Xiaowei Liu and Jin Zhang

Applied Mathematics and Computation, 2022, vol. 430, issue C

Abstract: For the singularly perturbed convection-diffusion equations, the uniform convergence of the finite element method on Bakhvalov-type mesh is still in its infancy. The challenge is how to handle the analysis on the last element mesh in the layer. In this manuscript, a streamline diffusion finite element method is properly defined on a Bakhvalov-type mesh. By means of delicate analysis of the terms on the last element mesh in the layer, we derive the supercloseness of almost order 2, which is consistent with the numerical experiments.

Keywords: Singular perturbation; Convection-diffusion equation; Bakhvalov-type mesh; Streamline diffusion finite element method; Supercloseness (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:430:y:2022:i:c:s0096300322003320

DOI: 10.1016/j.amc.2022.127258

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