Journal of Scientific Computing

, Volume 75, Issue 2, pp 597–624 | Cite as

Stormer-Numerov HDG Methods for Acoustic Waves

  • Bernardo Cockburn
  • Zhixing Fu
  • Allan Hungria
  • Liangyue Ji
  • Manuel A. Sánchez
  • Francisco-Javier Sayas
Article

Abstract

We introduce and analyze the first energy-conservative hybridizable discontinuous Galerkin method for the semidiscretization in space of the acoustic wave equation. We prove optimal convergence and superconvergence estimates for the semidiscrete method. We then introduce a two-step fourth-order-in-time Stormer-Numerov discretization and prove energy conservation and convergence estimates for the fully discrete method. In particular, we show that by using polynomial approximations of degree two, convergence of order four is obtained. Numerical experiments verifying that our theoretical orders of convergence are sharp are presented. We also show experiments comparing the method with dissipative methods of the same order.

Keywords

Hybridization Conservation of energy Discontinuous Galerkin Wave equation 

Mathematics Subject Classification

65M60 65M15 65M20 

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Bernardo Cockburn
    • 1
  • Zhixing Fu
    • 2
  • Allan Hungria
    • 2
  • Liangyue Ji
    • 1
  • Manuel A. Sánchez
    • 1
    • 3
  • Francisco-Javier Sayas
    • 2
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of Mathematical SciencesUniversity of DelawareNewarkUSA
  3. 3.Institute for Mathematical and Computational Engineering, School of Engineering and Faculty of MathematicsPontificia Universidad Católica de ChileSantiagoChile

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