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Guaranteed A Posteriori Error Estimates for a Staggered Discontinuous Galerkin Method

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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.

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Authors and Affiliations

  1. Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, SAR

    Eric T. Chung

  2. Department of Computational Science and Engineering, Yonsei University, Seoul, 03722, Republic of Korea

    Eun-Jae Park & Lina Zhao

Authors
  1. Eric T. Chung
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  2. Eun-Jae Park
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  3. Lina Zhao
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Correspondence to Eun-Jae Park.

Additional information

Eun-Jae Park: This author was supported by NRF-2015R1A5A1009350 and NRF-2016R1A2B4014358. Eric T. Chung’s research is partially supported by the Hong Kong RGC GRF (Project: 14301314) and the CUHK Direct Grant 2016-17.

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Chung, E.T., Park, EJ. & Zhao, L. Guaranteed A Posteriori Error Estimates for a Staggered Discontinuous Galerkin Method. J Sci Comput 75, 1079–1101 (2018). https://doi.org/10.1007/s10915-017-0575-8

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