Dispersive and dissipative errors in the DPG method with scaled norms for Helmholtz equation

J. Gopalakrishnan, I. Muga, N. Olivares

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

This paper studies the discontinuous Petrov Galerkin (DPG) method, where the test space is normed by a modified graph norm. The modification scales one of the terms in the graph norm by an arbitrary positive scaling parameter. The main finding is that as the parameter approaches zero, better results are obtained, under some circumstances, when the method is applied to the Helmholtz equation. The main tool used is a dispersion analysis on the multiple interacting stencils that form the DPG method. The analysis shows that the discrete wavenumbers of the method are complex, explaining the numerically observed artificial dissipation in the computed wave approximations. Since the DPG method is a nonstandard least-squares Galerkin method, its performance is compared with a standard least-squares method having a similar stencil.

Original languageEnglish
Pages (from-to)A20-A39
JournalSIAM Journal on Scientific Computing
Volume36
Issue number1
DOIs
StatePublished - 2014
Externally publishedYes

Keywords

  • Dispersion
  • Dissipation
  • Least squares
  • Quasi optimality
  • Resonance
  • Stencil

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