Guaranteed A Posteriori Error Estimates for a Staggered Discontinuous Galerkin Method

Eric T. Chung, Eun Jae Park, Lina Zhao

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper, we present for the first time guaranteed upper bounds for the staggered discontinuous Galerkin method for diffusion problems. Two error estimators are proposed for arbitrary polynomial degrees and provide an upper bound on the energy error of the scalar unknown and L2-error of the flux, respectively. Both error estimators are based on the potential and flux reconstructions. The potential reconstruction is given by a simple averaging operator. The equilibrated flux reconstruction can be found by solving local Neumann problems on elements sharing an edge with a Raviart–Thomas mixed method. Reliability and efficiency of the two a posteriori error estimators are proved. Numerical results are presented to validate the theoretical results.

Original languageEnglish
Pages (from-to)1079-1101
Number of pages23
JournalJournal of Scientific Computing
Volume75
Issue number2
DOIs
Publication statusPublished - 2018 May 1

Fingerprint

A Posteriori Error Estimates
Discontinuous Galerkin Method
Galerkin methods
Error Estimator
Upper bound
Fluxes
Averaging Operators
A Posteriori Error Estimators
Mixed Methods
Diffusion Problem
Neumann Problem
Sharing
Scalar
Unknown
Numerical Results
Polynomial
Arbitrary
Energy
Polynomials

All Science Journal Classification (ASJC) codes

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

Cite this

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Guaranteed A Posteriori Error Estimates for a Staggered Discontinuous Galerkin Method. / Chung, Eric T.; Park, Eun Jae; Zhao, Lina.

In: Journal of Scientific Computing, Vol. 75, No. 2, 01.05.2018, p. 1079-1101.

Research output: Contribution to journalArticle

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