Dear Aidyn, Many thanks for your email. Could I ask you to put in an issue for this? I have tried your example and get the same results but have not had a chance to look into why yet. If we have a record of it as an issue we can make sure we add it do our todo list! Regarding your question about eFactorTau. The tau is a parameter in the HDG approach and increasing the value penalises the jump in the function space to the point where as it tends to infinity you recover the classical Galerkin scheme. More details should be available in any paper on HDG. Best regards, Spencer.

On 2 Jan 2019, at 17:36, Aidyn Aitzhan <aidyn.b.aitzhan@gmail.com> wrote:

Dear All,

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 <Helmholtz2D.xml>_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users

Spencer Sherwin FREng, FRAeS Head, Aerodynamics, Director of Research Computing Service, Professor of Computational Fluid Mechanics, Department of Aeronautics, s.sherwin@imperial.ac.uk South Kensington Campus, Phone: +44 (0)20 7594 5052 Imperial College London, Fax: +44 (0)20 7594 1974 London, SW7 2AZ, UK http://www.imperial.ac.uk/people/s.sherwin/