Re: [Getfem-users] Reduction problems

[Yves Renard]

Dear Torquil,


The resulting finite element space when you supress the dof
corresponding to  intermediate points is not a partition of unity. So,
it is not able to approximate the constants. Consequently, I think, it
is normal that the solution is not well approximated. You have at least
to care that your reduction produces a finite element space which
reproduces the polynomial of degree less or equal to 1 to have a good
approximation.


Yves.


Le 15/07/2012 15:56, Torquil Macdonald Sørensen a écrit :
> Hi!
>
> I've started with the tests/laplacian.cc program, modified it a bit,
> and implemented an example reduction scheme. But whenever I use
> reduction, the solution is identical to zero apart from on the
> boundary, where I use Dirichlet conditions. In addition, I've also
> tried an approach using the Laplacian model, with the same incorrect
> results.
>
> In more detail, I have a square 2d domain and the mesh is:
>
> getfem::regular_unit_mesh(mesh, ref, bgeot::parallelepiped_geotrans(2,
> 1));
>
> On this mesh, I'm using FEM_QK(2,2) for both parts of the equation,
> and IM_GAUSS_PARALLELEPIPED(2,k) for k=3, but I've also tried k=4 and 5.
>
> The reduction scheme consists of using only the DOFs at the corners of
> the squares, and not the DOFs at the intermediate points along the
> edges or the central point of the square. I thought I'd try this as a
> simple example of reduction. The extention matrix E is the transpose
> of the reduction matrix R, and I do test that R*E is the identity, so
> that part should be OK.
>
> When using reduction, I make sure to use the "general Dirichlet"
> method in laplacian.cc, since the simplified approach won't work in
> that case.
>
> The program runs fine without error messages with and without
> reduction enabled, but as I mentioned, the solution is incorrect when
> using reduction (zero everywhere apart from the boundary).
>
> Any ideas about why this is so? Perhaps my reduction scheme is
> mathematically invalid for some reason, there is some bug in
> connection with reduction, or I've done something wrong?
>
> Best regards,
> Torquil Sørensen
>
>
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-- 

  Yves Renard (address@hidden)       tel : (33) 04.72.43.87.08
  Pole de Mathematiques, INSA-Lyon             fax : (33) 04.72.43.85.29
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