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Introduction to Discontinuous Galerkin Methods

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hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes

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Abstract

The purpose of this chapter is to present an overview of the construction of discontinuous Galerkin finite element methods for a general class of second-order partial differential equations with nonnegative characteristic form. This class of equations includes second-order elliptic and parabolic partial differential equations, ultra-parabolic equations, first-order hyperbolic problems, the Kolmogorov-Fokker-Planck equations of Brownian motion, the equations of boundary layer theory in hydrodynamics, and various other degenerate equations.

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Authors and Affiliations

  1. Department of Mathematics, University of Leicester, Leicester, UK

    Andrea Cangiani, Zhaonan Dong & Emmanuil H. Georgoulis

  2. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Emmanuil H. Georgoulis

  3. School of Mathematical Sciences, University of Nottingham, Nottingham, UK

    Paul Houston

Authors
  1. Andrea Cangiani
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  2. Zhaonan Dong
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  3. Emmanuil H. Georgoulis
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  4. Paul Houston
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Cangiani, A., Dong, Z., Georgoulis, E.H., Houston, P. (2017). Introduction to Discontinuous Galerkin Methods. In: hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-67673-9_2

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