Hello Wolfgang and Tobias, i tried the "shift" approach proposed by Tobias in an earlier email, but my convergence rate has not improved. I still get a convergence order of 1.5 no matter how I go about this (for a quadratic basis). is there some paper that describes the convergence properties of the streamline upwind DG method, and sheds some light on the reduced order of convergence? i was not able to find any references that explain this behavior...
i checked the nodal DG book by Hesthaven and Warburton (2007) and they do not mention anything about reduced orders of convergence when using the upwind fluxes. And my own 1D upwind DG code seems to converge as expected... thanks! -- Mihai ________________________________ Von: "[email protected]" <[email protected]> An: mihai alexe <[email protected]> CC: deal.ii <[email protected]> Gesendet: Montag, den 6. September 2010, 20:10:05 Uhr Betreff: Re: [deal.II] order of convergence for DG solver > I have modified the old version of step-12 (the pre-MeshWorker > variant) to determine the order of accuracy for the DG solver (on > uniform meshes). I am using piecewise quadratics and 4-point Gaussian > quadratures in the DG transport equation solver. I coded up the exact > solution (a simple, smooth function u = sin(2pi x) cos (2pi y)) and > modified the RHS and boundary conditions accordingly (and > double-checked everything for bugs/errors). The L2/L^\infty error > norms are computed in DGMethod<dim>::process_solution using 7-point > quadratures. In the end, the order of convergence that I am seeing is > only 1.5, instead of the 2nd order convergence that I was expecting. Not knowing much about the issue, but it's worth asking: Can one expect to get full order of convergence for the hyperbolic transport equation? My recollection was that, for example, using the streamline upwind method for this equation only yields order 1.5 as well. (This recollection may be entirely wrong, I just wanted to bring up the fundamental question.) W.
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