Constant free error bounds for nonuniform order discontinuous Galerkin finite-element approximation on locally refined meshes with hanging nodes

Mark Ainsworth, Richard Andrew Robert Rankin

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

We obtain fully computable constant free a posteriori error bounds on the broken energy seminorm and the discontinuous Galerkin (DG) norm of the error for nonuniform polynomial order symmetric interior penalty Galerkin, nonsymmetric interior penalty Galerkin and incomplete interior penalty Galerkin finite-element approximations of a linear second-order elliptic problem on meshes containing hanging nodes and comprised of triangular elements. The estimators are completely free of unknown constants and provide guaranteed numerical bounds on the broken energy seminorm and the DG norm of the error. These estimators are also shown to provide a lower bound for the broken energy seminorm and the DG norm of the error up to a constant and higher-order data oscillation terms.
LanguageEnglish
Pages254-280
Number of pages27
JournalIMA Journal of Numerical Analysis
Volume31
Issue number1
DOIs
Publication statusPublished - 2011

Fingerprint

Interior Penalty
Seminorm
Discontinuous Galerkin
Galerkin Approximation
Finite Element Approximation
Error Bounds
Mesh
Norm
Galerkin
Vertex of a graph
Energy
Estimator
Second-order Elliptic Problems
Triangular Element
Linear Order
Oscillation
Higher Order
Lower bound
Unknown
Polynomial

Keywords

  • finite-element analysis
  • hanging nodes
  • Galerkin finite-element approximation

Cite this

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Constant free error bounds for nonuniform order discontinuous Galerkin finite-element approximation on locally refined meshes with hanging nodes. / Ainsworth, Mark; Rankin, Richard Andrew Robert.

In: IMA Journal of Numerical Analysis, Vol. 31, No. 1, 2011, p. 254-280.

Research output: Contribution to journalArticle

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