I found why it's not going further down ! It was just that the GPL file saved is with a precision of 6 digits which corresponds with the error per dofs when I norm my error plot by the solution.
Thanks for the help everyone ! On Friday, October 11, 2019 at 9:51:40 AM UTC+2, Félix Bunel wrote: > > Hi thank you very much ! > > That was the problem I believe ! THANKS A LOT ! Now the error go down > quadratically at the beginning. > > Then it goes up again linearly which i find very strange... I believe it's > because I haven't set enough precision in the solving process or maybe i'm > reaching machine precision... > > > > On Thursday, October 10, 2019 at 10:12:07 PM UTC+2, luca.heltai wrote: >> >> Dear Felix, >> >> by any chance, did you take a look at step 10? >> >> https://www.dealii.org/current/doxygen/deal.II/step_10.html >> >> This step explains a little bit what to do when you want to solve on >> curved domains with high order finite elements. In particular, you need to >> ensure that the mapping you are using (from the reference element to the >> current element) is at least of the same order of your finite element >> method, if you want to achieve the correct convergence rates. In your case, >> you are using a MappingQ1 (the default mapping, if you don’t specify >> anything). With that, you won’t go beyond 2nd order in L2. If you use >> MappingQ2, you should see again the optimal convergence rates. >> >> Best, >> Luca. >> >> > On 10 Oct 2019, at 14:11, Félix Bunel <bunel...@gmail.com> wrote: >> > >> > Thanks for your answer ! >> > >> > I'm working in 2D on a disk ! >> > >> > This is my mesh on the 4 cycle of refinement (which I never use in >> practice because it's not refined enough for what I want to do). >> > >> > <Auto Generated Inline Image 1.png> >> > >> > I don't think I have a mapping object... >> > What i do to initalize my system on phi is : >> > //On génère le dofhandler >> > phi_dof_handler.distribute_dofs (phi_fe); >> > >> > //On génère les conditions aux bords >> > phi_constraints.clear(); >> > DoFTools::make_hanging_node_constraints(phi_dof_handler, >> phi_constraints); >> > VectorTools::interpolate_boundary_values(phi_dof_handler, >> > 0, >> > ZeroFunction<2>(1), >> > phi_constraints >> > ); >> > >> > //On créer le sparsity pattern >> > DynamicSparsityPattern dsp(phi_dof_handler.n_dofs()); >> > DoFTools::make_sparsity_pattern (phi_dof_handler, dsp); >> > phi_sparsity_pattern.copy_from(dsp); >> > >> > //On resize les objets à la bonne taille >> > phi_system_matrix.reinit (phi_sparsity_pattern); >> > phi_solution.reinit (phi_dof_handler.n_dofs()); >> > phi_old_solution.reinit (phi_dof_handler.n_dofs()); >> > phi_system_rhs.reinit (phi_dof_handler.n_dofs()); >> > >> > //On affiche les infos intéressantes >> > std::cout << YELLOW << " Nombre de degrés de liberté pour les >> angles : " >> > << RESET << WHITE << phi_dof_handler.n_dofs() << RESET >> > << std::endl; >> > >> > >> > >> > Le jeudi 10 octobre 2019 14:00:23 UTC+2, Bruno Blais a écrit : >> > A quick question, since you are working on a sphere, are you specifying >> a mapping of the same order as your phi? >> > >> > On Wednesday, 9 October 2019 08:57:45 UTC-4, Félix Bunel wrote: >> > Hello everyone. >> > >> > I'm having some trouble to understand the convergence rate i'm >> observing in my code. >> > >> > Here is what i'm solving : >> > >> > - I'm in 2D on a round mesh. >> > - I'm solving a simple Poisson equation on this mesh for a variable >> named Phi the solution is known for this and is 1-x^2-y^2 >> > - With this solution phi I'm then solving a Stokes equation that has >> special terms that depends on phi. >> > >> > For the stokes problem i'm using the usual mixed fe element as such : >> > stokes_fe(FE_Q<2>(2), 2, >> > FE_Q<2>(1), 1), >> > So second order for the speeds and first order for the pressure (just >> like in the boussinesq problem from the tutorials. >> > >> > For the poisson/phi problem, i'm using FE_Q<2> also >> > initialized as such : >> > phi_fe (2), >> > So second order. >> > >> > For a special case, I have a known solution which is u=v=0 and p of the >> form 1-x^2-y^2 (just like phi) >> > And i have solved this on multiple refinement cycle which gives me >> different number of dofs and cellsize. >> > >> > >> > The thing is, when I plot the error as a function of the maximum cell >> diameter, I get a quadratic convergence rate for the speed, and a linear >> rate for P and phi. >> > What surprises me is that I don't have a quadratic convergence rate for >> my poisson/\phi problem even though I used >> > phi_fe (2), >> > >> > My norm is the L2 norm which is simply sqrt(sum(error**2))). I'm >> computing it with python after exporting the solution as a gpl file. >> > Here are the graphs : >> > >> > >> > >> > I have also tried >> > phi_fe (1), >> > >> > But in this case I don't even have convergence for the speed. >> > >> > >> > >> > In my integration part, I have always used >> > QGauss<2> quadrature_formula(4); >> > which is equal to degree+2. >> > >> > So here are my questions : >> > >> > 1- Is this convergence rate the one i'm expecting for a poisson >> equation (phi problem) ? >> > >> > 2- If no, any idea why I don't have the correct convergence rate ? >> > >> > 3- In the tutorial step 31, a degree of 2 is used for the temperature >> (which is very similar to my phi), is there some reason for that choice >> (just like using degree+1 for the speed and degree for the pressure in a >> stokes problem...) >> > >> > Thanks in advance. >> > >> > -- >> > The deal.II project is located at http://www.dealii.org/ >> > For mailing list/forum options, see >> https://groups.google.com/d/forum/dealii?hl=en >> > --- >> > You received this message because you are subscribed to the Google >> Groups "deal.II User Group" group. >> > To unsubscribe from this group and stop receiving emails from it, send >> an email to dea...@googlegroups.com. >> > To view this discussion on the web visit >> https://groups.google.com/d/msgid/dealii/966a3637-8ca8-462a-bf7a-621746c9c6ad%40googlegroups.com. >> >> >> > <Auto Generated Inline Image 1.png> >> >> -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. 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