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Article
Dispersive and Dissipative Errors in the DPG Method with Scaled Norms for Helmholtz Equation
SIAM Journal on Scientific Computing
  • Jay Gopalakrishnan, Portland State University
  • Ignacio Muga, Pontificia Universidad Catolica de Chile
  • Nicole Olivares, Portland State University
Document Type
Article
Publication Date
1-1-2014
Subjects
  • Helmholtz equation,
  • Numerical analysis,
  • Galerkin methods
Disciplines
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.
Description

This is the publisher's final PDF. First Published in SIAM Journal on Scientific Computing in volume 36 and number 1, published by the Society of Industrial and Applied Mathematics (SIAM) . Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

This article can be found online at: http://dx.doi.org/10.1137/130918186

DOI
10.1137/130918186
Persistent Identifier
http://archives.pdx.edu/ds/psu/10584
Citation Information
Gopalakrishnan, J., Muga, I. and Olivares, N. (2014). Dispersive and Dissipative Errors in the DPG Method with Scaled Norms for Helmholtz Equation. Vol. 36, No. 1, pp. A20–A39.