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Space-Time Discontinuous Galerkin Method for the Problem of Linear Elasticity

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Numerical Mathematics and Advanced Applications - ENUMATH 2013

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 103))

Abstract

The subject of this paper is the numerical solution of the problem of dynamic linear elasticity by several time-discretization techniques based on the application of the discontinuous Galerkin (DG) method in space. In the formulation of the numerical scheme, the nonsymmetric, symmetric and incomplete versions of the discretization of the elasticity term and the interior and boundary penalty are used. The DG space discretization is combined with the backward-Euler, second-order backward-difference formula and DG time discretization. Finally, we present some test problems.

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References

  1. P.G. Ciarlet, The Finite Element Method for Elliptic Problems (North-Holland, Amsterdam, 1978)

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  2. B. Cockburn, G.E. Karniadakis, C.W. Shu (Eds.), Discontinuous Galerkin Methods, Theory, Computation and Applications (Springer, Berlin, 2000)

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  4. B. Rivière, Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations: Theory and Implementation (SIAM, Philadelphia, 2008)

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Author information

Authors and Affiliations

  1. Charles University in Prague, Faculty of Mathematics and Physics, Sokolovská 83, 186 75, Praha 8, Czech Republic

    Martin Hadrava, Miloslav Feistauer & Adam Kosík

  2. Institute of Thermomechanics, The Academy of Sciences of the Czech Republic, v. v. i., Dolejškova 1402/5, 182 00, Praha 8, Czech Republic

    Jaromír Horáček

Authors
  1. Martin Hadrava
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  2. Miloslav Feistauer
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  3. Jaromír Horáček
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  4. Adam Kosík
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Corresponding author

Correspondence to Martin Hadrava .

Editor information

Editors and Affiliations

  1. MATHICSE-ANMC, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Assyr Abdulle

  2. SB MATHICSE CMCS, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Simone Deparis

  3. SB MATHICSE ANCHP, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Daniel Kressner

  4. SB MATHICSE CSQI, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Fabio Nobile

  5. SB MATHICSE GR-PI, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Marco Picasso

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Hadrava, M., Feistauer, M., Horáček, J., Kosík, A. (2015). Space-Time Discontinuous Galerkin Method for the Problem of Linear Elasticity. In: Abdulle, A., Deparis, S., Kressner, D., Nobile, F., Picasso, M. (eds) Numerical Mathematics and Advanced Applications - ENUMATH 2013. Lecture Notes in Computational Science and Engineering, vol 103. Springer, Cham. https://doi.org/10.1007/978-3-319-10705-9_11

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