Re: [Getfem-users] Math behind product of three variables in high-level generic assembly

[Yves Renard]

Dear Jan,

If you declare the term to be linear, there should be only one assembly
(the matrix) otherwise there will be an assembly for the matrix term and
one for the right hand side (residual).

And yes, the matrix is indeed  M_{ij} = \int f \phi_i \phi_j  for \phi_i the
shape functions and the second order is preserved for a sufficient
order of the integration method (this kind of result can be found for
instance is Ciarlet's book "The finite element method for elliptic
problems").

Best regards,

Yves.


Le 02/05/2016 08:49, Jan Wróblewski a écrit :
> Hello everyone,
>
> I am interested in the math behind computing a part of high-level generic
> assembly term “f*u*Test_u”, where u is the FEM variable and f is initialized
> fem data on the same mesh.
> How is the matrix assembled in this case?
> Why are there multiple iterations (at least multiple "Trace 2 in
> getfem_models.cc, line 2607: Global generic assembly")?
> Is creating of the matrix done by using the selected integration method to
> compute integral of f*b1*b2 (where b1 and b2 are appropriate base functions
> from the FEM space)?
> And, most importantly, if selected integration method is good enough and FEM
> space is classical 2nd order polynomials, is 2nd order of precision still
> achieved?
>
> I look forward to your responses,
>
> Jan Wroblewski
>
>
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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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  http://math.univ-lyon1.fr/~renard

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