A balanced finite element method for a system of singularly perturbed reaction-diffusion two-point boundary value problems
type: Item
instance of: scholarly article
title: A balanced finite element method for a system of singularly perturbed reaction-diffusion two-point boundary value problems
zbMATH Open document ID: 1333.65084
author: Runchang Lin
author: Martin Stynes
published in: Numerical Algorithms
publication date: 2016-01-25T00:00:00Z
review text: The authors analyze a system of linear coupled reaction-diffusion equations, where each equation is a two-point boundary value problem and all equations share the same small diffusion coefficient. They propose a finite element method using piecewise quadratic splines. The norm associated with the proposed method is stronger than the usual energy norm and ``balanced''. Numerical examples are also discussed.
reviewed by: Răzvan Răducanu
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 65L11
zbMATH DE Number: 6535405
zbMATH Keywords: singular perturbation
zbMATH Keywords: balanced norm
zbMATH Keywords: Shishkin mesh
zbMATH Keywords: spline interpolant
zbMATH Keywords: system of linear coupled reaction-diffusion equations
zbMATH Keywords: two-point boundary value problem
zbMATH Keywords: finite element method
zbMATH Keywords: numerical example
MaRDI profile type: Publication
full work available at URL: s11075-015-9969-6
OpenAlex ID: W1983272004
cites work: A first-order system Petrov–Galerkin discretization for a reaction–diffusion problem on a fitted mesh
cites work: A Balanced Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems
cites work: Analysis of a FEM for a coupled system of singularly perturbed reaction-diffusion equations
cites work: Layer-adapted meshes for reaction-convection-diffusion problems
cites work: Layer-adapted meshes for a linear system of coupled singularly perturbed reaction-diffusion problems
cites work: Numerical Solution of Systems of Singularly Perturbed Differential Equations
cites work: Convergence and stability in balanced norms of finite element methods on Shishkin meshes for reaction‐diffusion problems
cites work: Robust Numerical Methods for Singularly Perturbed Differential Equations
cites work: Q3592409
DOI: 10.1007/S11075-015-9969-6
description: scientific article; zbMATH DE number 6535405