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
