I was working on Helmholtz equation solver and found, that DG projection produces errors on periodic boundaries (XML file attached). Check the following log:

=======================================================================
            EquationType: Helmholtz
            Session Name: Helmholtz2D
            Spatial Dim.: 2
      Max SEM Exp. Order: 7
          Expansion Dim.: 2
          Advection Type:
         Projection Type: Continuous Galerkin
                  Lambda: 0
        Forcing func [0]: -(Lambda + 2*alpha*alpha)*sin(alpha*x)*sin(alpha*y)
=======================================================================
Writing: "Helmholtz2D.fld" (0.0222731s, XML)
-------------------------------------------
Total Computation Time = 4s
-------------------------------------------
L 2 error (variable u) : 0.00017053
L inf error (variable u) : 2.93867e-05

=======================================================================
            EquationType: Helmholtz
            Session Name: Helmholtz2D
            Spatial Dim.: 2
      Max SEM Exp. Order: 7
          Expansion Dim.: 2
          Advection Type:
         Projection Type: Discontinuous Galerkin
                  Lambda: 0
        Forcing func [0]: -(Lambda + 2*alpha*alpha)*sin(alpha*x)*sin(alpha*y)
=======================================================================
Writing: "Helmholtz2D.fld" (0.0316639s, XML)
-------------------------------------------
Total Computation Time = 5s
-------------------------------------------
L 2 error (variable u) : 3.94935
L inf error (variable u) : 1.00002

As we can see L2 and Linf of DG solution are too high. Plotting the results I figured out that the error is on the boundaries.

I have got the same results for both nektar-master version and nektar-4.4.1.

Am I doing something incorrect?

One more short question, there is a factor "eFactorTau" in discontinuous Helmholtz solver, which is not present in continuous one. What is this factor responsible for?

I cannot run the solver not specifying it, but I get the same results for factors[StdRegions::eFactorTau] = 1.0 and factors[StdRegions::eFactorTau] = 1000.

Thank you very much and Happy New Year,

Aidyn