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).
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.
>>
>
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