An a posteriori error estimate for finite element approximations of a singularly perturbed advection-diffusion problem
type: Item
instance of: scholarly article
title: An a posteriori error estimate for finite element approximations of a singularly perturbed advection-diffusion problem
zbMATH Open document ID: 0889.65113
DOI: 10.1016/S0377-0427(97)00191-X
published in: Journal of Computational and Applied Mathematics
publication date: 1998-06-02T00:00:00Z
review text: This paper deals with an a posteriori error estimator for an important nonselfadjoint problem, i.e. a singularly perturbed advection-diffusion problem in two dimensions. Based on a complementary variational principle, the author shows that the error in an energy norm is bounded by the sum of the weighted \(L^2\)-norms of solutions to a set of independent variational problems, each defined on only one element of a given partition. These local problems can be solved numerically by a finite element method on a refined mesh of the original. It is shown that the numerical solutions of the local variational problems define an approximate upper error bound which differs from the theoretical upper bound by a higher-order term than the true error. The numerical results presented here show that the computed error bounds are tight for a wide range of values of \(\varepsilon\) and always over-estimate the true errors.
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 1121351
zbMATH Keywords: singular perturbation
zbMATH Keywords: numerical examples
zbMATH Keywords: advection-diffusion problem
zbMATH Keywords: finite element method
zbMATH Keywords: error bounds
author: Song Wang
reviewed by: Pavol Chocholatý
describes a project that uses: CRAIG
describes a project that uses: LSQR
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1121351