Discontinuous Galerkin error estimation for hyperbolic problems on unstructured triangular meshes

Mahboub Baccouch, Slimane Adjerid

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

We extend the error analysis of Adjerid and Baccouch [1,2] for the discontinuous Galerkin discretization error to variable-coefficient linear hyperbolic problems as well as nonlinear hyperbolic problems on unstructured meshes. We further extend this analysis to transient hyperbolic problems and prove that the local superconvergence results presented in [1] still hold for both steady and transient variable-coefficient linear and nonlinear problems. This local error analysis allows us to construct asymptotically correct a posteriori error estimates by solving local hyperbolic problems with no boundary conditions on each element of general unstructured meshes. We illustrate the superconvergence and the efficiency of our a posteriori error estimates by showing computational results for several linear and nonlinear numerical examples.

Original languageEnglish (US)
Pages (from-to)162-177
Number of pages16
JournalComputer Methods in Applied Mechanics and Engineering
Volume200
Issue number1-4
DOIs
StatePublished - Jan 1 2011

Fingerprint

Error analysis
mesh
error analysis
coefficients
estimates
Boundary conditions
boundary conditions

Keywords

  • A posteriori error estimation
  • Discontinuous Galerkin method
  • Hyperbolic problems
  • Superconvergence
  • Transient convection problems
  • Unstructured meshes

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

Cite this

Discontinuous Galerkin error estimation for hyperbolic problems on unstructured triangular meshes. / Baccouch, Mahboub; Adjerid, Slimane.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 200, No. 1-4, 01.01.2011, p. 162-177.

Research output: Contribution to journalArticle

@article{51dedd9bc376403ebd051bebea1b3ae8,
title = "Discontinuous Galerkin error estimation for hyperbolic problems on unstructured triangular meshes",
abstract = "We extend the error analysis of Adjerid and Baccouch [1,2] for the discontinuous Galerkin discretization error to variable-coefficient linear hyperbolic problems as well as nonlinear hyperbolic problems on unstructured meshes. We further extend this analysis to transient hyperbolic problems and prove that the local superconvergence results presented in [1] still hold for both steady and transient variable-coefficient linear and nonlinear problems. This local error analysis allows us to construct asymptotically correct a posteriori error estimates by solving local hyperbolic problems with no boundary conditions on each element of general unstructured meshes. We illustrate the superconvergence and the efficiency of our a posteriori error estimates by showing computational results for several linear and nonlinear numerical examples.",
keywords = "A posteriori error estimation, Discontinuous Galerkin method, Hyperbolic problems, Superconvergence, Transient convection problems, Unstructured meshes",
author = "Mahboub Baccouch and Slimane Adjerid",
year = "2011",
month = "1",
day = "1",
doi = "10.1016/j.cma.2010.08.002",
language = "English (US)",
volume = "200",
pages = "162--177",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0374-2830",
publisher = "Elsevier",
number = "1-4",

}

TY - JOUR

T1 - Discontinuous Galerkin error estimation for hyperbolic problems on unstructured triangular meshes

AU - Baccouch, Mahboub

AU - Adjerid, Slimane

PY - 2011/1/1

Y1 - 2011/1/1

N2 - We extend the error analysis of Adjerid and Baccouch [1,2] for the discontinuous Galerkin discretization error to variable-coefficient linear hyperbolic problems as well as nonlinear hyperbolic problems on unstructured meshes. We further extend this analysis to transient hyperbolic problems and prove that the local superconvergence results presented in [1] still hold for both steady and transient variable-coefficient linear and nonlinear problems. This local error analysis allows us to construct asymptotically correct a posteriori error estimates by solving local hyperbolic problems with no boundary conditions on each element of general unstructured meshes. We illustrate the superconvergence and the efficiency of our a posteriori error estimates by showing computational results for several linear and nonlinear numerical examples.

AB - We extend the error analysis of Adjerid and Baccouch [1,2] for the discontinuous Galerkin discretization error to variable-coefficient linear hyperbolic problems as well as nonlinear hyperbolic problems on unstructured meshes. We further extend this analysis to transient hyperbolic problems and prove that the local superconvergence results presented in [1] still hold for both steady and transient variable-coefficient linear and nonlinear problems. This local error analysis allows us to construct asymptotically correct a posteriori error estimates by solving local hyperbolic problems with no boundary conditions on each element of general unstructured meshes. We illustrate the superconvergence and the efficiency of our a posteriori error estimates by showing computational results for several linear and nonlinear numerical examples.

KW - A posteriori error estimation

KW - Discontinuous Galerkin method

KW - Hyperbolic problems

KW - Superconvergence

KW - Transient convection problems

KW - Unstructured meshes

UR - http://www.scopus.com/inward/record.url?scp=78649634945&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78649634945&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2010.08.002

DO - 10.1016/j.cma.2010.08.002

M3 - Article

AN - SCOPUS:78649634945

VL - 200

SP - 162

EP - 177

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0374-2830

IS - 1-4

ER -