A note on the convergence rate of the finite element method for singularly perturbed problems using the Shishkin mesh

DOI10.1016/S0096-3003(02)00338-7zbMath1024.65069OpenAlexW2119299672MaRDI QIDQ1399760

Christos Xenophontos

Publication date: 30 July 2003

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0096-3003(02)00338-7

zbMATH Keywords

convergencefinite element methoderror boundsShishkin meshsingularly perturbation

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Linear boundary value problems for ordinary differential equations (34B05) Singular perturbations for ordinary differential equations (34E15) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (2)

A numerical study on the finite element solution of singularly perturbed systems of reaction-diffusion problems ⋮ A brief survey on numerical methods for solving singularly perturbed problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The h, p and h-p versions of the finite element method in 1 dimension. II. The error analysis of the h- and h-p versions
• The \(hp\) finite element method for problems in mechanics with boundary layers
• On the Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems in Two and One Dimensions
• hp FEM for Reaction-Diffusion Equations I: Robust Exponential Convergence
• Thehp finite element method for singularly perturbed problems in nonsmooth domains
• THE hp FINITE ELEMENT METHOD FOR SINGULARLY PERTURBED PROBLEMS IN SMOOTH DOMAINS
• On piecewise-uniform meshes for upwind- and central-difference operators for solving singularly perturbed problems
• Finite element superconvergence approximation for one-dimensional singularly perturbed problems
• The $p$ and $hp$ versions of the finite element method for problems with boundary layers
• Uniform approximation of singularly perturbed reaction-diffusion problems by the finite element method on a Shishkin mesh

This page was built for publication: A note on the convergence rate of the finite element method for singularly perturbed problems using the Shishkin mesh