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Error Control for Discontinuous Galerkin Methods for First Order Hyperbolic Problems

  • Emmanuil H. GeorgoulisEmail author
  • Edward Hall
  • Charalambos Makridakis
Chapter
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 157)

Abstract

An a posteriori error bound for a first order linear hyperbolic problem, with constant advection coefficient, discretized by the discontinuous Galerkin method is presented. The bound is derived using a suitable reconstruction framework, but it is essentially of residual-type. For simplicity, the special case of the mesh having one characteristic face per element is the focus of discussion, although some comments on possible extensions to general meshes are given. Numerical experiments verify the reliability and the efficiency of the estimator.

Keywords

A posteriori error bounds Discontinous Galerkin method Hyperbolic problem 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Emmanuil H. Georgoulis
    • 1
    Email author
  • Edward Hall
    • 2
  • Charalambos Makridakis
    • 3
  1. 1.Department of MathematicsUniversity of LeicesterLeicesterUK
  2. 2.School of Mathematical SciencesUniversity of NottinghamUniversity Park, NottinghamUK
  3. 3.Department of Applied MathematicsUniversity of CreteHeraklion-CreteGreece

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