A parameter robust Petrov-Galerkin scheme for advection-diffusion-reaction equations
type: Item
instance of: scholarly article
title: A parameter robust Petrov-Galerkin scheme for advection-diffusion-reaction equations
zbMATH Open document ID: 1208.65171
author: C. de Falco
author: Eugene O'Riordan
published in: Numerical Algorithms
publication date: 2011-01-28T00:00:00Z
review text: This paper deals with a singularly perturbed differential equation \[ -(\varepsilon(x) u')'+ a(x) u'+ b(x) u= f(x),\quad x\in (0,1)\setminus\{d_i\}^m_{i=1}, \] where the variable diffusion coefficient \(\varepsilon\) and the other data \(a\), \(b\), \(f\), can be discontinuous at the points \(d_i\in (0,1)\). A parameter-uniform numerical method for such problem is constructed. The authors use a combination of a fitted finite difference operator and a fitted layer-adapted mesh to simplify the analysis of a high-order parameter-uniform globally convergent numerical method. Four numerical examples are given.
reviewed by: Pavol Chocholatý
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65L60
zbMATH DE Number: 5842765
zbMATH Keywords: interior layers
zbMATH Keywords: discontinuous diffusion
zbMATH Keywords: Petrov-Galerkin
MaRDI profile type: Publication
full work available at URL: s11075-010-9376-y
OpenAlex ID: W2066930753
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DOI: 10.1007/S11075-010-9376-Y
description: scientific article; zbMATH DE number 5842765