Uniform-in-time superconvergence of the HDG methods for the acoustic wave equation

Bernardo Cockburn, Vincent Quenneville-Bélair

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

Abstract

We present the first a priori error analysis of the hybridizable discontinuous Galerkin methods for the acoustic equation in the time-continuous case. We show that the velocity and the gradient converge with the optimal order of k + 1 in the L2-norm uniformly in time whenever polynomials of degree k ≥ 0 are used. Finally, we show how to take advantage of this local postprocessing to obtain an approximation to the original scalar unknown also converging with order k+2 for k ≥ 1. This puts on firm mathematical ground the numerical results obtained in J. Comput. Phys.

Original languageEnglish (US)
Pages (from-to)65-85
Number of pages21
JournalMathematics of Computation
Volume83
Issue number285
DOIs
StatePublished - Jan 1 2014

Keywords

  • Discontinuous galerkin methods
  • Hybridization
  • Hyperbolic problems
  • Superconvergence

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