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SIAM Journal on Scientific Computing

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Helmholtz equation, Numerical analysis, Galerkin methods


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.


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.

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