Stormer-Numerov HDG Methods for Acoustic Waves

Bernardo Cockburn, Zhixing Fu, Allan Hungria, Liangyue Ji, Manuel A. Sánchez, Francisco Javier Sayas

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)597-624
Number of pages28
JournalJournal of Scientific Computing
Volume75
Issue number2
DOIs
StatePublished - May 1 2018

Keywords

  • Conservation of energy
  • Discontinuous Galerkin
  • Hybridization
  • Wave equation

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