  We consider the discontinuous Petrov-Galerkin (DPG) method, wher the test
space is normed by a modified graph norm. The modificatio scales one of the
terms in the graph norm by an arbitrary positive scaling parameter. Studying
the application of the method to the Helmholtz equation, we find that better
results are obtained, under some circumstances, as the scaling parameter
approaches a limiting value. We perform 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, we compare its
performance with a standard least-squares method.
