The discontinuous Galerkin method for two-dimensional hyperbolic problems part II: A posteriori error estimation

Slimane Adjerid, Mahboub Baccouch

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

In this manuscript we construct simple, efficient and asymptotically correct a posteriori error estimates for discontinuous finite element solutions of scalar first-order hyperbolic partial differential problems on triangular meshes. We explicitly write the basis functions for the error spaces corresponding to several finite element spaces. The leading term of the discretization error on each triangle is estimated by solving a local problem. We also show global superconvergence for discontinuous solutions on triangular meshes. The a posteriori error estimates are tested on several linear and nonlinear problems to show their efficiency and accuracy under mesh refinement for smooth and discontinuous solutions.

Original languageEnglish (US)
Pages (from-to)15-49
Number of pages35
JournalJournal of Scientific Computing
Volume38
Issue number1
DOIs
StatePublished - Jan 1 2009

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A Posteriori Error Estimation
Discontinuous Solutions
Hyperbolic Problems
Triangular Mesh
A Posteriori Error Estimates
Discontinuous Galerkin Method
Galerkin methods
Error analysis
Discontinuous Finite Elements
Superconvergence
Discretization Error
Mesh Refinement
Finite Element Solution
Smooth Solution
Basis Functions
Nonlinear Problem
Triangle
Scalar
Finite Element
First-order

Keywords

  • A posteriori error estimation
  • Discontinuous Galerkin method
  • Hyperbolic problems
  • Superconvergence

ASJC Scopus subject areas

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

Cite this

The discontinuous Galerkin method for two-dimensional hyperbolic problems part II : A posteriori error estimation. / Adjerid, Slimane; Baccouch, Mahboub.

In: Journal of Scientific Computing, Vol. 38, No. 1, 01.01.2009, p. 15-49.

Research output: Contribution to journalArticle

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