Superconvergence of finite element method for singularly perturbed convection-diffusion equations in 1D

DOI10.1016/j.aml.2019.06.018zbMath1464.65133OpenAlexW2956078375MaRDI QIDQ2275199

Jin Zhang, Xiao-Wei Liu

Publication date: 2 October 2019

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2019.06.018

zbMATH Keywords

singular perturbationfinite element methodconvection-diffusion equationsuperconvergenceShishkin mesh

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (9)

Supercloseness of linear streamline diffusion finite element method on Bakhvalov-type mesh for singularly perturbed convection-diffusion equation in 1D ⋮ Convergence of a finite element method on a Bakhvalov‐type mesh for a singularly perturbed convection–diffusion equation in <scp>2D</scp> ⋮ A higher‐order hybrid spline difference method on adaptive mesh for solving singularly perturbed parabolic reaction–diffusion problems with robin‐boundary conditions ⋮ Supercloseness analysis of the linear finite element method for a singularly perturbed convection-diffusion problem on Vulanović-Bakhvalov mesh ⋮ A semi-adaptive preservative scheme for a fractional quenching convective-diffusion problem ⋮ Optimal order of uniform convergence for finite element method on Bakhvalov-type meshes ⋮ Supercloseness and postprocessing for linear finite element method on Bakhvalov-type meshes ⋮ Supercloseness of linear finite element method on Bakhvalov-type meshes for singularly perturbed convection-diffusion equation in 1D ⋮ A unified study on superconvergence analysis of Galerkin FEM for singularly perturbed systems of multiscale nature

Cites Work

• Fitted Numerical Methods For Singular Perturbation Problems
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• Finite element superconvergence approximation for one-dimensional singularly perturbed problems

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