A Posteriori Local Discontinuous Galerkin Error Estimation for Two-Dimensional Convection–Diffusion Problems

Mahboub Baccouch, Slimane Adjerid

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We present a simple, efficient, and asymptotically correct a posteriori error estimates for a minimal dissipation local discontinuous Galerkin method applied to two-dimensional diffusion and convection–diffusion problems on rectangular meshes. The finite element spaces are obtained by performing a local error analysis and a posteriori error estimates are computed by solving local problems on each element. We present computational results for several problems to show the efficiency and accuracy of our error estimates. It is shown that even in the presence of boundary layers our error estimates converge to the true error under mesh refinement when Shishkin meshes are used.

Original languageEnglish (US)
Pages (from-to)399-430
Number of pages32
JournalJournal of Scientific Computing
Volume62
Issue number2
DOIs
StatePublished - Jan 1 2014

Fingerprint

Convection-diffusion
Discontinuous Galerkin
Error Estimation
Error analysis
A Posteriori Error Estimates
Error Estimates
Local Discontinuous Galerkin Method
Shishkin Mesh
Mesh Refinement
Error Analysis
Computational Results
Boundary Layer
Dissipation
Mesh
Finite Element
Converge
Galerkin methods
Boundary layers

Keywords

  • A posteriori error estimates
  • Convection–diffusion problems
  • Local discontinuous Galerkin method
  • Superconvergence

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Cite this

A Posteriori Local Discontinuous Galerkin Error Estimation for Two-Dimensional Convection–Diffusion Problems. / Baccouch, Mahboub; Adjerid, Slimane.

In: Journal of Scientific Computing, Vol. 62, No. 2, 01.01.2014, p. 399-430.

Research output: Contribution to journalArticle

@article{2f2090d332264862a92fe48d4143c9f8,
title = "A Posteriori Local Discontinuous Galerkin Error Estimation for Two-Dimensional Convection–Diffusion Problems",
abstract = "We present a simple, efficient, and asymptotically correct a posteriori error estimates for a minimal dissipation local discontinuous Galerkin method applied to two-dimensional diffusion and convection–diffusion problems on rectangular meshes. The finite element spaces are obtained by performing a local error analysis and a posteriori error estimates are computed by solving local problems on each element. We present computational results for several problems to show the efficiency and accuracy of our error estimates. It is shown that even in the presence of boundary layers our error estimates converge to the true error under mesh refinement when Shishkin meshes are used.",
keywords = "A posteriori error estimates, Convection–diffusion problems, Local discontinuous Galerkin method, Superconvergence",
author = "Mahboub Baccouch and Slimane Adjerid",
year = "2014",
month = "1",
day = "1",
doi = "10.1007/s10915-014-9861-x",
language = "English (US)",
volume = "62",
pages = "399--430",
journal = "Journal of Scientific Computing",
issn = "0885-7474",
publisher = "Springer New York",
number = "2",

}

TY - JOUR

T1 - A Posteriori Local Discontinuous Galerkin Error Estimation for Two-Dimensional Convection–Diffusion Problems

AU - Baccouch, Mahboub

AU - Adjerid, Slimane

PY - 2014/1/1

Y1 - 2014/1/1

N2 - We present a simple, efficient, and asymptotically correct a posteriori error estimates for a minimal dissipation local discontinuous Galerkin method applied to two-dimensional diffusion and convection–diffusion problems on rectangular meshes. The finite element spaces are obtained by performing a local error analysis and a posteriori error estimates are computed by solving local problems on each element. We present computational results for several problems to show the efficiency and accuracy of our error estimates. It is shown that even in the presence of boundary layers our error estimates converge to the true error under mesh refinement when Shishkin meshes are used.

AB - We present a simple, efficient, and asymptotically correct a posteriori error estimates for a minimal dissipation local discontinuous Galerkin method applied to two-dimensional diffusion and convection–diffusion problems on rectangular meshes. The finite element spaces are obtained by performing a local error analysis and a posteriori error estimates are computed by solving local problems on each element. We present computational results for several problems to show the efficiency and accuracy of our error estimates. It is shown that even in the presence of boundary layers our error estimates converge to the true error under mesh refinement when Shishkin meshes are used.

KW - A posteriori error estimates

KW - Convection–diffusion problems

KW - Local discontinuous Galerkin method

KW - Superconvergence

UR - http://www.scopus.com/inward/record.url?scp=84921069112&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84921069112&partnerID=8YFLogxK

U2 - 10.1007/s10915-014-9861-x

DO - 10.1007/s10915-014-9861-x

M3 - Article

VL - 62

SP - 399

EP - 430

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

SN - 0885-7474

IS - 2

ER -