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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