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Implementation Aspects

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hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes

Part of the book series: SpringerBriefs in Mathematics ((BRIEFSMATH))

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Abstract

In this chapter we outline the key implementation aspects of exploiting discontinuous Galerkin finite element methods on general computational meshes consisting of polytopic elements: mesh generation, construction of the elemental polynomial basis, and numerical integration. We also present some numerical examples to highlight the sharpness of the a priori error bounds derived in this volume for both a steady advection-diffusion-reaction problem and a (degenerate) parabolic problem.

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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). Implementation Aspects. 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_6

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