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FEM 2017: Advanced Finite Element Methods with Applications pp 341–370Cite as

A Stabilized Space–Time Finite Element Method for the Wave Equation

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE,volume 128)

Abstract

We consider a space–time variational formulation of the wave equation by including integration by parts also in the time variable. A standard finite element discretization by using lowest order piecewise linear continuous functions then requires a CFL condition to ensure stability. To overcome this restriction, and following the work of Zlotnik (Convergence rate estimates of finite-element methods for second-order hyperbolic equations. In: Numerical methods and applications, pp. 155–220. CRC, Boca Raton, 1994), we consider, in the case of tensor–product space–time discretizations, a stabilized variational problem which is unconditionally stable. We provide a stability and error analysis, and some numerical results which confirm the theoretical findings.

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Fig. 17.2

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, TU Graz, Graz, Austria

    Olaf Steinbach & Marco Zank

Authors
  1. Olaf Steinbach
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  2. Marco Zank
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Corresponding author

Correspondence to Olaf Steinbach .

Editor information

Editors and Affiliations

  1. Institut für Mathematik & Computergestützte Simulation, Universität der Bundeswehr München, Neubiberg, Germany

    Prof. Dr. Thomas Apel

  2. Institute for Computational Mathematics, Johannes Kepler University Linz, Linz, Austria

    Prof. Dr. Ulrich Langer

  3. Fakultät für Mathematik, TU Chemnitz, Chemnitz, Germany

    Prof. Dr. Arnd Meyer

  4. Institut für Angewandte Mathematik, Technische Universität Graz, Graz, Austria

    Prof. Dr. Olaf Steinbach

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Steinbach, O., Zank, M. (2019). A Stabilized Space–Time Finite Element Method for the Wave Equation. In: Apel, T., Langer, U., Meyer, A., Steinbach, O. (eds) Advanced Finite Element Methods with Applications. FEM 2017. Lecture Notes in Computational Science and Engineering, vol 128. Springer, Cham. https://doi.org/10.1007/978-3-030-14244-5_17

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