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A Posteriori Error Estimates for HDG Methods

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Abstract

We present the first a posteriori error analysis of the so-called hybridizable discontinuous Galerkin (HDG) methods for second-order elliptic problems. We show that the error in the flux can be controlled by only two terms. The first term captures the so-called data oscillation. The second solely depends on the difference between the trace of the scalar approximation and the corresponding numerical trace. Numerical experiments verifying the reliability and efficiency of the estimate in two-space dimensions are presented.

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Authors and Affiliations

  1. School of Mathematics, University of Minnesota, Minneapolis, MN, USA

    Bernardo Cockburn & Wujun Zhang

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  1. Bernardo Cockburn
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  2. Wujun Zhang
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Correspondence to Wujun Zhang.

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Cockburn, B., Zhang, W. A Posteriori Error Estimates for HDG Methods. J Sci Comput 51, 582–607 (2012). https://doi.org/10.1007/s10915-011-9522-2

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  • DOI: https://doi.org/10.1007/s10915-011-9522-2

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