I looked for the source of the error, and found that it is due to the
fact that I call Mesh::all_second_order() after refining the mesh by,
MeshRefinement::uniformly_refine (n_refinements). It corrupts the
internal data structure or something in EquationSystems object. It
doesn't even save the right solution when I call
EquationSystems.write(...). When I call all_second_order before refining
the mesh, everything works perfectly.
I will implement a new function for integration over cylindrical domain
for error estimate.
Thanks for your help,
Yusuke
On 05/16/2012 10:06 AM, Derek Gaston wrote:
> Quadrature rule should really have nothing to do with it. If you are really
> passing in the _exact_ same solution as the one you are computing it should
> compute zero error (to within machine precision).
>
> Can you create a small example solving something simple that demonstrates the
> problem?
>
> Derek
>
> On May 15, 2012, at 11:06 PM, Yusuke Sakamoto wrote:
>
>> Just reply to myself, I realized that as long as vr, vz, and p values
>> are the same for two different equation systems, the error should be
>> zero, whether the domain is normal 2D or axisymmetric 2D. The source of
>> the error is that the quadrature order used in ExactSolution to compute
>> the reference values is different from the quadrature order used in
>> MeshFunction to compute the coarse values. I am not sure how
>> ExactSolution and MeshFunction determine the quadrature rule. Am I doing
>> something wrong here, or is this a bug in Libmesh?
>>
>> Yusuke
>>
>> On 05/14/2012 05:53 PM, Yusuke Sakamoto wrote:
>>> Dear all,
>>>
>>> I am trying to carry out the convergence analysis on the 2D axisymmetric
>>> mesh. The problem is a simple Stokes flow. Before comparing the result
>>> to the reference mesh, I compared the solution to itself.
>>>
>>> // Compare the computed solution to the reference solution
>>> ExactSolution ExSol(equation_systems);
>>> ExSol.attach_reference_solution(&equation_systems);
>>>
>>> string sys_name("Cell");
>>> string var_name;
>>>
>>> var_name = "vr";
>>> ExSol.compute_error(sys_name, var_name);
>>> Real h1_vr = ExSol.h1_error(sys_name, var_name);
>>>
>>> var_name = "vz";
>>> ExSol.compute_error(sys_name, var_name);
>>> Real h1_vz = ExSol.h1_error(sys_name, var_name);
>>>
>>> var_name = "p";
>>> ExSol.compute_error(sys_name, var_name);
>>> Real L2_p = ExSol.l2_error(sys_name, var_name);
>>>
>>> The error should be zero, but the result is not very good...
>>>
>>> H1 vr: 0.0189777
>>> H1 vz: 1.74623e-09
>>> L2 p: 2.2159e-08
>>>
>>> Is this because internally, libmesh differentiate and integrate the
>>> error over normal 2D domain? If so, which part should I modify?
>>>
>>> Thanks,
>>>
>>> Yusuke
>>>
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