Hello all, 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. Is there anything that I am missing? I expect that DG would converge quadratically, given order 2 basis functions and sufficient accuracy in the inner product computations and linear system solver (residual norm acceptable for convergence is 10^-14)...
One more thing - if I use a piecewise linear basis function set, then the convergence is linear as expected. Thanks in advance for your advice! -- Mihai
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