Optimal error estimate and superconvergence of the DG method for first-order hyperbolic problems

  • Zhang T
  • Li Z
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Abstract

We consider the original discontinuous Galerkin method for the first-order hyperbolic problems in d-dimensional space. We show that, when the method uses polynomials of degree k, the L2-error estimate is of order k+1 provided the triangulation is made of rectangular elements satisfying certain conditions. Further, we show the O(h2k+1)-order superconvergence for the error on average on some suitably chosen subdomains (including the whole domain) and their outflow faces. Moreover, we also establish a derivative recovery formula for the approximation of the convection directional derivative which is superconvergent with order k+1. © 2010 Elsevier B.V. All rights reserved.

Author-supplied keywords

  • Discontinuous Galerkin method
  • First-order hyperbolic problem
  • Optimal error estimate
  • Superconvergence

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Authors

  • Tie Zhang

  • Zheng Li

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