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Continuous Finite-Elements on Non-Conforming Grids Using Discontinuous Galerkin Stabilization

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Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 77))

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Abstract

In this paper we present a new idea to stabilize Continuous Galerkin Schemes on grids with hanging nodes by using Discontinuous Galerkin (DG) approximations. We derive an a posteriori error estimate for a class of DG schemes including the CDG and CDG2 methods and apply this to standard test cases for CG methods such a the reentrant corner.

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Author information

Authors and Affiliations

  1. University of Warwick, Coventry, UK

    Andreas Dedner

  2. National Center for Atmospheric Research, 1850 Table Mesa Drive, Boulder, CO, 80305, USA

    Robert Klöfkorn

  3. University of Freiburg, Freiburg im Breisgau, Germany

    Mirko Kränkel

Authors
  1. Andreas Dedner
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  2. Robert Klöfkorn
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  3. Mirko Kränkel
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Corresponding author

Correspondence to Robert Klöfkorn .

Editor information

Editors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Jürgen Fuhrmann

  2. Institute Comp. Applied Mathematics, University of Münster Center for Nonlinear Sciences (CeNoS ), Münster, Germany

    Mario Ohlberger

  3. Inst. Appl. Analysis and Num. Simulation, University of Stuttgart, Stuttgart, Germany

    Christian Rohde

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© 2014 Springer International Publishing Switzerland

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Dedner, A., Klöfkorn, R., Kränkel, M. (2014). Continuous Finite-Elements on Non-Conforming Grids Using Discontinuous Galerkin Stabilization. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Springer Proceedings in Mathematics & Statistics, vol 77. Springer, Cham. https://doi.org/10.1007/978-3-319-05684-5_19

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