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.
Bibliographical noteFunding 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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All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Numerical Analysis
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics