Fully computable error bounds for discontinuous Galerkin finite element approximations on meshes with an arbitrary number of levels of hanging nodes

M. Ainsworth, R. Rankin

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

We obtain fully computable a posteriori error bounds on the broken energy seminorm and discontinuous Galerkin norm (DG-norm) of the error in first order symmetric interior penalty Galerkin (SIPG), nonsymmetric interior penalty Galerkin (NIPG), and incomplete interior penalty Galerkin (IIPG) finite element approximations of a linear second order elliptic problem on meshes containing an arbitrary number of levels of 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 DG-norm of the error. These estimators are also shown to provide a lower bound for the broken energy seminorm and DG-norm of the error up to a constant and higher order data oscillation terms. We also obtain an explicit computable bound for the value of the interior penalty parameter needed to ensure the existence of the discontinuous Galerkin finite element approximation for all versions of the method.
LanguageEnglish
Pages4112-4141
Number of pages29
JournalSIAM Journal on Numerical Analysis
Volume47
Issue number6
DOIs
Publication statusPublished - 15 Jan 2010

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

Keywords

  • a posteriori error estimation
  • discontinuous Galerkin method
  • computable error bounds

Cite this

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Fully computable error bounds for discontinuous Galerkin finite element approximations on meshes with an arbitrary number of levels of hanging nodes. / Ainsworth, M.; Rankin, R.

In: SIAM Journal on Numerical Analysis, Vol. 47, No. 6, 15.01.2010, p. 4112-4141.

Research output: Contribution to journalArticle

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