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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>
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