Guaranteed A Posteriori Error Estimates for a Staggered Discontinuous Galerkin Method

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)1079-1101
Journal / PublicationJournal of Scientific Computing
Volume75
Issue number2
Publication statusPublished - 1 May 2018
Externally publishedYes

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.

Research Area(s)

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

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