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Journal of Scientific Computing

, Volume 75, Issue 2, pp 1079–1101 | Cite as

Guaranteed A Posteriori Error Estimates for a Staggered Discontinuous Galerkin Method

  • Eric T. Chung
  • Eun-Jae Park
  • Lina Zhao
Article
  • 352 Downloads

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 \(L^2\)-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.

Keywords

Staggered grid Discontinuous Galerkin method Guaranteed upper bound A posteriori error estimators 

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of MathematicsThe Chinese University of Hong KongShatinHong Kong, SAR
  2. 2.Department of Computational Science and EngineeringYonsei UniversitySeoulRepublic of Korea

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