I tested the modified code with uniform refinement and exact_sol.extra_quadrature_order(1). I printed out both l2 error and h1 error and got
time = 0.025, refinement step = 0, elements = 10240, l2_error = 0.002885, h1_error = 0.239394 Time = 0.025, refinement step = 1, elements = 40960, l2_error = 0.002643, h1_error = 0.207076 Time = 0.025, refinement step = 2, elements = 163840, l2_error = 0.002596, h1_error = 0.210480 Time = 0.025, refinement step = 3, elements = 655360, l2_error = 0.002575, h1_error = 0.214309 Time = 0.025, refinement step = 4, elements = 2621440, l2_error = 0.002569, h1_error = 0.215482 We can see l2_error monotonically decreases, however h1_error does not. What is the possible reason? Thanks. --Junchao Zhang On Thu, Jan 28, 2016 at 10:53 PM, Junchao Zhang <junchao.zh...@gmail.com> wrote: > I found an example of exact_sol.extra_quadrature_order() > in adaptivity_ex3.C. > > Also, I found if I refined the mesh upfront (though the -n_refinements > argument, e.g., set it to 5), L2 error would monotonically decrease with > more refinements. Previously, I set n_refinements to 0 to get a small > 10-elements-11-nodes mesh at the first time step for debugging purpose. Now > I know that is questionable in view of error analysis as Roy explained. > > --Junchao Zhang > > On Thu, Jan 28, 2016 at 6:50 PM, Derek Gaston <fried...@gmail.com> wrote: > >> Also: it can depend on integration error in the integration of the L2 >> Error. We're still using quadrature to integrate... so if that quadrature >> is poor you can "miss" solution features on a coarse grid that then show up >> as you refine the mesh (which refines the quadrature too) leading to higher >> error. >> >> One way to combat that is to use the "extra quadrature order" capability >> when computing the L2 Norm of the error... it allows you to "fine up" your >> quadrature to give you a better integral on the coarse mesh. I don't >> remember exactly how to do that on the moment (currently on my phone on the >> subway)... so if you snoop around a bit and don't find it... write back in. >> >> Derek >> On Thu, Jan 28, 2016 at 1:36 PM Roy Stogner <royst...@ices.utexas.edu> >> wrote: >> >>> >>> On Wed, 27 Jan 2016, Junchao Zhang wrote: >>> >>> > Time = 0.025, refinement step = 0, elements = 10, l2_error = >>> 0.443873 >>> > Time = 0.025, refinement step = 1, elements = 40, l2_error = >>> 0.045196 >>> > Time = 0.025, refinement step = 2, elements = 160, l2_error = >>> 0.131169 >>> > Time = 0.025, refinement step = 3, elements = 640, l2_error = >>> 0.116789 >>> > Time = 0.025, refinement step = 4, elements = 2560, l2_error = >>> 0.118175 >>> > >>> > >>> > I am curious why sometimes L2 error gets bigger, e.g., from r_step 1 to >>> > r_step 2. Don't more refinements give smaller errors? >>> >>> If your solve's discretization error is your only source of error, and >>> if you're solving a self-adjoint problem, then more refinements should >>> *always* give you smaller errors. >>> >>> This problem isn't self-adjoint, so the convection term can cause >>> convergence to be more erratic, but I don't think that's the problem >>> here. >>> >>> The problem might be that you've got two sources of discretization >>> error here: the discretization for the solve, and the discretization >>> for the initial conditions. If you project the initial conditions and >>> then refine, rather than refine and then project, you won't actually >>> have improved your approximation of the initial conditions. So you >>> won't converge to the exact solution you want, you'll converge to the >>> solution of the PDE with the wrong initial conditions. >>> --- >>> Roy >>> >>> >>> ------------------------------------------------------------------------------ >>> Site24x7 APM Insight: Get Deep Visibility into Application Performance >>> APM + Mobile APM + RUM: Monitor 3 App instances at just $35/Month >>> Monitor end-to-end web transactions and take corrective actions now >>> Troubleshoot faster and improve end-user experience. Signup Now! >>> http://pubads.g.doubleclick.net/gampad/clk?id=267308311&iu=/4140 >>> _______________________________________________ >>> Libmesh-users mailing list >>> Libmesh-users@lists.sourceforge.net >>> https://lists.sourceforge.net/lists/listinfo/libmesh-users >>> >> > ------------------------------------------------------------------------------ Site24x7 APM Insight: Get Deep Visibility into Application Performance APM + Mobile APM + RUM: Monitor 3 App instances at just $35/Month Monitor end-to-end web transactions and take corrective actions now Troubleshoot faster and improve end-user experience. Signup Now! http://pubads.g.doubleclick.net/gampad/clk?id=267308311&iu=/4140 _______________________________________________ Libmesh-users mailing list Libmesh-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/libmesh-users
