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Advanced Finite Element Methods and Applications pp 27–56Cite as

Domain Decomposition Preconditioning for High Order Hybrid Discontinuous Galerkin Methods on Tetrahedral Meshes

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Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 66))

Abstract

Hybrid discontinuous Galerkin methods are popular discretization methods in applications from fluid dynamics and many others. Often large scale linear systems arising from elliptic operators have to be solved. We show that standard p-version domain decomposition techniques can be applied, but we have to develop new technical tools to prove poly-logarithmic condition number estimates, in particular on tetrahedral meshes.

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Authors and Affiliations

  1. Institut für Analysis und Scientific Computing, TU Wien, Wiedner Hauptstrasse 8–10, 1040, Wien, Austria

    Joachim Schöberl

  2. Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, 52056, Aachen, Germany

    Christoph Lehrenfeld

Authors
  1. Joachim Schöberl
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  2. Christoph Lehrenfeld
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Correspondence to Joachim Schöberl .

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Editors and Affiliations

  1. Inst. Mathematik und Bauinformatik, Universität der Bundeswehr München, Neubiberg, 85579, Germany

    Thomas Apel

  2. Institut für Numerische Mathematik, Technische Universität Graz, Steyrergasse 30, Graz, 8010, Austria

    Olaf Steinbach

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Schöberl, J., Lehrenfeld, C. (2013). Domain Decomposition Preconditioning for High Order Hybrid Discontinuous Galerkin Methods on Tetrahedral Meshes. In: Apel, T., Steinbach, O. (eds) Advanced Finite Element Methods and Applications. Lecture Notes in Applied and Computational Mechanics, vol 66. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30316-6_2

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  • DOI: https://doi.org/10.1007/978-3-642-30316-6_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30315-9

  • Online ISBN: 978-3-642-30316-6

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