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 <javascript:>> > 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 <javascript:>. > > 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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