Supercloseness of linear finite element method on Bakhvalov-type meshes for singularly perturbed convection-diffusion equation in 1D
type: Item
instance of: scholarly article
title: Supercloseness of linear finite element method on Bakhvalov-type meshes for singularly perturbed convection-diffusion equation in 1D
zbMATH Open document ID: 1451.65101
author: Jin Zhang
author: Xiaowei Liu
published in: Applied Mathematics Letters
publication date: 2020-10-08T00:00:00Z
review text: The authors use a linear finite element method on Bakhvalov-type meshes to solve a singularly perturbed two-point boundary value problem (in one dimension). Thanks to a novel interpolation to the solution, a new supercloseness result is derived and proved.
reviewed by: Abdallah Bradji
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L11
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 7258397
zbMATH Keywords: singularly perturbed problem
zbMATH Keywords: convection-diffusion equation
zbMATH Keywords: Bakhvalov-type mesh
zbMATH Keywords: finite element method
zbMATH Keywords: supercloseness property
MaRDI profile type: Publication
full work available at URL: j.aml.2020.106624
OpenAlex ID: W3041412907
cites work: Fitted numerical methods for singular perturbation problems. Error estimates in the maximum norm for linear problems in one and two dimensions.
cites work: Robust Numerical Methods for Singularly Perturbed Differential Equations
cites work: Layer-adapted meshes for reaction-convection-diffusion problems
cites work: Q5610080
cites work: Q4697772
cites work: The SDFEM for a Convection-Diffusion Problem with a Boundary Layer: Optimal Error Analysis and Enhancement of Accuracy
cites work: Optimal Order $L^2$ Error Estimate of SDFEM on Shishkin Triangular Meshes for Singularly Perturbed Convection-Diffusion Equations
cites work: Pointwise estimates of SDFEM on Shishkin triangular meshes for problems with exponential layers
cites work: Singularly perturbed problems with characteristic layers. Supercloseness and postprocessing
cites work: Supercloseness on graded meshes for \({\mathcal Q}_1\) finite element approximation of a reaction-diffusion equation
cites work: Analysis of SDFEM on Shishkin triangular meshes and hybrid meshes for problems with characteristic layers
cites work: Supercloseness of the SDFEM on Shishkin triangular meshes for problems with exponential layers
cites work: Supercloseness of continuous interior penalty method for convection-diffusion problems with characteristic layers
cites work: Supercloseness of edge stabilization on Shishkin rectangular meshes for convection–diffusion problems with exponential layers
cites work: Supercloseness of the continuous interior penalty method for singularly perturbed problems in 1D: vertex-cell interpolation
cites work: Supercloseness of continuous interior penalty methods on Shishkin triangular meshes and hybrid meshes for singularly perturbed problems with characteristic layers
cites work: The finite element methods for elliptic problems.
cites work: Error estimates for linear finite elements on Bakhvalov-type meshes.
cites work: Uniform convergence with respect to a small parameter of a scheme with central difference on refining grids
cites work: The Mathematical Theory of Finite Element Methods
cites work: Superconvergence of finite element method for singularly perturbed convection-diffusion equations in 1D
DOI: 10.1016/J.AML.2020.106624
description: scientific article; zbMATH DE number 7258397