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We consider the discontinuous Petrov-Galerkin (DPG) method, wher the testspace is normed by a modified graph norm. The modificatio scales one of theterms in the graph norm by an arbitrary positive scaling parameter. Studyingthe application of the method to the Helmholtz equation, we find that betterresults are obtained, under some circumstances, as the scaling parameterapproaches a limiting value. We perform a dispersion analysis on the multipleinteracting stencils that form the DPG method. The analysis shows that thediscrete wavenumbers of the method are complex, explaining the numericallyobserved artificial dissipation in the computed wave approximations. Since theDPG method is a nonstandard least-squares Galerkin method, we compare itsperformance with a standard least-squares method.

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