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A posteriori error estimation for hybridized mixed and discontinuous Galerkin methods

Augsburger Schriften zur Mathematik, Physik und Informatik , Bd. 19

Johannes Neher

ISBN 978-3-8325-3088-4
105 pages, year of publication: 2012
price: 33.50 €
There is a variety of finite element based methods applicable to the discretization of second order elliptic boundary value problems in mixed form. However, it is expensive to solve the resulting discrete linear system due to its size and its algebraic structure. Hybridization serves as a tool to circumvent these difficulties. Furthermore hybridization is an elegant concept to establish connections among various finite element methods.

In this work connections between the methods and their hybridized counterparts are established after showing the link between three different formulations of the elliptic model problem. The main part of the work contains the development of a reliable a posteriori error estimator, which is applicable to all of the methods above. This estimator is the key ingredient of an adaptive numerical approximation of the original boundary value problem. Finally, a number of numerical tests is discussed in order to exhibit the performance of the adaptive hybridized methods.

Keywords:
  • adaptivity
  • discontinuous Galerkin methods
  • mixed methods
  • hybridized methods
  • elliptic problems

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